Soviet elections often had many candidates, indeed many parties. Of course ALL parties and candidates had to be approved by the appropriate bodies of the CPSU making them pretty much puppets of the CPSU (which was the whole point).

In addition to Alex's excellent summary of how the USSR worked (which many European countries are getting very close to, e.g. in the Netherlands every voter is recorded, which may or may not be linked to his actual votes cast (in case of electronic voting, they certainly have the option but whether it's actually done is not known to me), people might well vote for local people, especially in local and regional elections, hoping their village/town candidate might be able to do something for them in the higher levels of the party bureaucracy eventually.

I have found this text about Soviet elections turnout on the site of the Moscow State University. I do not know who is the author.

Some points:

• In election one could strike all the candidates and write in one's own. There was a place for doing so in the ballot. The voting list would not be considered invalid after that (unlike modern Russia). If the majority did so, the manually written in person would be considered elected.

• Sometimes there were instances when the inhabitants of a living block would agree not to go to elections for instance untill the state would not make a capital reconstruction of their house. This would be extraordinary incident reported to the highest levels and all the demands would be satisfied immediately. Because of this custom some elder people still say "lets not to go to elections because this and this not done" The author says this is because the people do not understand that Soviet rule is over and this would not work any more.

Just as in the elections themselves, what actually went on in the USSR did not necessarily match what the rules and law said was going on. People might be cautious that if you weren't seen voting, there would be consequences no matter what the law said.

There have been many factors, indeed.

• People were unaware that other approaches exist. It is hard to believe for a Westerner, but the Kommunist propaganda worked very well: they really believed this is the only way for voting, and the „rotting West“ has even worse situation;
• The vast majority of people believed they could change at least something on the local level. E.g., electing a „better“ kommunist would help him to lobby the interest of a town on the „republican“ level;
• „Donos“ (Wikipedia, RUS), a habit of filing complaints to KGB (or Trade Union, or a local Party Nucleus), as means for winning a competition, was widespread across the entire Soviet system. If you've seen something and didn't complain, there will be a complain on you (for non-complaining). So, if Alice didn't attend „elections“ and Bob has seen it, either there will be Bob's complain on Alice or Charlie's complain on both Alice (for non-attending) and Bob (for non-complaining);
  • This does not mean that KGB will necessarily come to take you to GULAG concentration camp the very next night at 4AM. But you may see some unexpected obstacles in your future activities: the smaller one is inability to get a free ticket to „pansionat“ (Holiday House) for your kids the next summer. There tickets were given by „Trade Unions“ to the most loyal „citizens“.
• Those who really understood the situation, also realized that those 99.9% votes were fake. Regardless of whether or not you attend, your „vote“ will be counted;
• Don't discount the importance of a chance of buying deficit foods, too. Despite of miserable „salaries“, the deficit was even stronger. Most of people had had unused money, and attending the „elections“ was a great opportunity to buy at least something. Also, I would oppose the point of «the practice of offering food at the voting posts … reached the height in late USSR», to me it was the opposite: it started diminishing in late 1980's and almost lost by 1990 when there was nothing left to offer.

Summary

The system has been built this way, there was literally no escape from it.

Just read the law.

The Положение о выборах в Верховный Совет СССР (1945) that is The statue of elections to the Supreme Council of the USSR (1945) states:

Статья 106. Если поданное количество голосов по округу составляет меньше половины числа избирателей, имеющих право голосова­ния по этому округу, Окружная избирательная комиссия по выборам в Совет Союза или по выборам в Совет Национальностей отмечает об этом о протоколе и сообщает Немедленно в Центральную избирательную комиссию и в Избирательную комиссию по выборам в Совет Национальностей Cоюзной, автономной рес­публики, автономной области или националь­ного округа. В этом случае Центральная из­бирательная комиссия назначает новые выбо­ры не позднее, чем в двухнедельный срок после первых выборов.

slightly edited google translation:

Article 106. If the specified number of votes in the electoral district is less than half the number of voters eligible to vote in this district, the district election commission for elections to the Council of the Union and for elections to the Council of Nationalities notes the fact in the protocol and reports immediately to the Central Election Commission and Electoral Commission for elections to the Council of Nationalities of the union republic, the autonomous republic, the autonomous region or the national area. In this case, the Central Election Commission shall appoint new elections no later than two weeks after the first election.

in other words, if the turnout was low they would have to repeat it all over again within two weeks.

That alone is a good reason to encourage participants.

Even in USA your participation in elections is recorded: as you come to the booth, your name is marked in the logs. It was most certainly recorded in USSR, and, because of the "propiska" (the mandatory registration of your address with the local government), the officials knew exactly where to find those who showed their disloyalty to the government by refusing to participate vote. I've heard first-hand accounts from lower-level CPSU officials who were dispatched to those addresses at the end of the election day to find out if those who missed the vote had an acceptable excuse (such as illness) and remind them of their civic duties if they didn't.

Those who served in the Army had no choice at all. Some divisions had "voting competitions": the units competed to see who would vote faster. The soldiers lined up under their officers' supervision and when the command was given to vote at the start of election time, the lines would run through the booths, registering their votes exactly as ordered as quickly as possible. The unit that was the slowest was reprimanded for lack of discipline.

In short, participation in the elections, as well as the choices provided, weren't a matter of the citizen's free will in the USSR. It was a "balagan", a show. I'm not quite sure which purpose it served. Was it make-believe to show its citizens that their decisions mattered? Was it make-believe to show foreigners that USSR was a democracy? Was it jading its citizens against the idea of democracy? ("You think they vote in USA? Yeah, right, they vote for show just like you do here.") Was it only to detect insufficiently loyal citizens? Was it some combination of the reasons above?

When you are talking about participation and the numbers of votes for the candidate, you should take into account that these numbers were mostly fake. Nobody really counted. Another thing which is difficult to understand for Westerners is the permanent feeling of fear. People knew that there was a record, who voted and who did not. They also believed that it can be tracked how they voted.

And this really happened. You come to the polling place, you show your ID (internal passport), they will give you the paper, and make a notice that you voted.

Closer to the evening they would go search for people who did not vote, knock to their doors, and ask to vote. Nobody wanted trouble (with very few exceptions).

Anyway, people wanted their friends, neighbors and colleagues see them near the voting boots, not speaking of those plain cloth people who were always hanging around.

(This answer is a participant account).

From a comment by Sassa NF:

In real life I asked my parents why they would still go and vote - I asked this after USSR collapsed. The answer was exactly what I said - "are you mad? It would instantly be known and there would be consequences"

I became curious and asked my mother. She was born in early 1950s, so her reply covers the years 1969 to 1986. (In 1986 the Perestroika began and the Soviet regime started loosening up).

She said she first attended elections, out of curiosity, in 1969, when she had become able to vote. She hardly attended any elections afterwards, up to 1989. There were no repercussions. She was a usual Soviet person, with a university degree (an economist).

Her brother was a Communist Party member, and served in a district committee apparatus actually (a kind of sub-Mayor's Office apparatus responsible for governing a district in Yekaterinburg, then Sverdlovsk). Furthermore, it was part of his duties to ensure the presence of "propaganda materials" of various sorts on the streets, as far as I remember.

The only reprimands she got were reprimands by her mother, my grandma, who reproached her mildly for being so negligent while her brother was sitting through the day in a voting station (he was on an election commission). He never suffered due to his sister's absenteeism.

My father never voted either. He woke up early on the day of voting and went to the voting station to buy some of the deficit goods before they've been sold out. That was quite an incentive. A Western person would find it hard to imagine what an incentive it was in a deficit economy. After buying the goods, he made an about-turn and went home, having done sweet FA in terms of actual voting.

He told me that hypothetically one could be reprimanded at work for not voting, and he suspects that one could fail to get some of the better amenities available to those who fawned to the system. That is, you could fail to obtain a tourist tour to a country in Eastern Europe. But he did not consider that a serious thing. He was not a Party member, and belevied the Black Sea coast to be a-okay for a family trip, if in exchange you could shirk at least partly from participating in the circus.

What was the reason for such high turnout?

I tried to google for some texts written by professional historians on this topic. A quick googling brought up one small article, the author of which (Alexander Fokin) mentions the importance of propaganda and the factor of people being cautious not to fall out of line, not to attract attention by their absenteeism. But was that hard enough incentive in the post-Stalin years? I also found a dissertation by a Podosinnikov Andrei, covering the period from 1950-1970. It states that the elections were widely propagandized and turned into a kind of holiday for the majority of the population. In that holiday atmosphere, it was just keeping with a tradition to go and "vote", even though the majority of the people understood the phoniness of the process.

I am sure that in the Stalin era my parents would have attended the elections: the fear was strong while Stalin was alive. But I have no reason to doubt their accounts of the 1970s-80s period. One could suggest that there was a wide-ranging manipulation of statistics by low-level commissions. My perfunctory googling brought up no works on that count. If I found some in the future, I'd expand my answer. Until then, it'll remain basically a couple of retold first-hand accounts.

References:

• Александр Фокин: Выборы в СССР в 1960-1970-е гг.: симуляция или элемент демократии?

• Подосинников Андрей Юрьевич. ИСТОРИЧЕСКИЙ ОПЫТ ПРОВЕДЕНИЯ ВЫБОРОВ В ОРГАНЫ НАРОДНОГО ПРЕДСТАВИТЕЛЬСТВА НА ТЕРРИТОРИИ КУРСКОЙ ОБЛАСТИ В 1950-1970-е гг.