Regarding your second question, it does save the airlines money in many situations. As simple as that. Of course, they still need some staff but it's a game of numbers and we can talk all we want about the baggage drop, it still makes a sizable difference.

Online check-in means far fewer passengers to process, possibly 50% or more on short-haul low-cost flights in Europe. And for the passengers who still require assistance, the ground handling agents have fewer things to do and can go faster. Besides, many airlines now push passengers to take only hand luggage (by charging extra for hold luggage) and automate both the check-in at the airport or the baggage drop itself so that the only staff left are “helpers” standing around (maybe 1 for 3 or 4 automated stations) and you don't have any option but to check-in at a machine.

In that case, you might as well do it online.

How does this benefit me?

My impression is that it doesn't. As with many automated systems of that kind (actually, this applies both to online check-in and to the automated check-in), it is inherently connected to a couple of problems:

• For a start, you have to supply the equipment. While that is usually not a problem at home, I rarely have more than a smartphone with me while traveling, and using web-pages designed for use on a PC monitor rather than on a smartphone is usually a pain.
• On a fair number of occasions, the service will not work as intended.
• If that happens, the hassle of solving it is upon you, rather than the airport staff.
• Furthermore, it is primarily upon you alone, because even contacting someone to ask for help is yet another effort to make.
• Even if it does work, the latter point applies, as anything that is unclear will have to remain subject to speculation, as you cannot simply ask the check-in agent.

Maybe checking in online gives you an edge when it comes to getting a specific seat, or a larger number of adjacent seats. On the other hand, I have rarely encountered a problem with the latter requirement; check-in agents almost always seemed to be able to somehow find or clear a sufficient set of adjacent seats.

Therefore, I suspect airlines only pretend it is a great feature for passengers, while the primary motivation is ...

How does it benefit the airline?

It probably saves loads of money. As with any aspect of customer service that can be abandoned, airlines can save on service staff. Dropping one's bag typically only takes a fraction of the time that the full check-in process does (unless one exceeds weight limits or similar), so I do think manning the bag drop counter is much less of an effort. Possibly, beside the net working time on the activity of checking in, some customers are even deterred from asking some other questions that they would otherwise direct at the check-in agent, thus saving even more time and employees.

Airlines always overbooked their flights to maximized the seats. And even sell seats on the last hour of the flights. They do this because there are a lot of scenarios where passenger didn't show up on their flights for many reasons like connecting flights delayed, passengers offloaded due to visa issues, group travel cancellation, etc.

With that said, checking in the passenger online gives them a clear picture of how many passengers are really flying on that specific time. It gives them opportunity to sell tickets or increase/decrease the price of it based on the number of seats available. It will also give the staff a rough idea if they can still get the airline discount tickets for that flight as staff tickets usually have the lowest priority in terms of getting a seat.

I check-in as early as possible because I can sometimes score an upgrade at a price that I'm willing to pay, pay baggage fees in advance, and make it more likely that I'll get a seat that I want.

If flying domestically in the US, I can also confirm that I have Precheck listed on the boarding pass.

 Checking in is the best way to confirm your ticket is valid.

In the case of traditional network airlines, who all have to conform to the worldwide IATA ticketing standards agreed in the 1970s, you will only be able to check in for a flight if your flight coupon for that flight is valid and is in an "open" state ready to be uplifted by the operating carrier.

If you have made any changes to your ticket, and these changes have not been re-ticketed properly, check-in may be the first time you find out. Obviously the earlier you find that out the better, particularly if the ticket was issued by a different carrier to the next operating carrier. At the airport, if your ticketing carrier has no presence, it may simply not be possible for the ticket to be re-issued in time for your reserved travel.

As an example, a friend of mine recently had to buy a walk up full economy fare at just over €1000 on a oneway flight from Helsinki to London because his airline had not processed a change properly and had failed to re-issue his ticket. He had a reservation on the flight, everything appeared fine, but he was unable to check in. The operating carrier was a different airline to the one who issued the ticket, and had no control over the e-ticket, and the ticketing airline was not available in time to remedy the problem. The only option, if he wanted to be on time for work, was to purchase a new ticket there and then. [His money was refunded in full by the ticketing carrier later that week as they accepted it was their fault, but still could be annoying.]

This situation can also happen even when there were no changes, but your ticket required some manual intervention to be issued. There are also concerns over "passive sectors" where the link between the ticketing airline and another airline failed at time reservations were made and instead the PNR was manually adjusted to include those flight segments.

Some airlines process upgrades and offloads prioritized by check-in time.

British Airways for instance, in the event of an oversold cabin, prioritizes the last person to check-in for an offload and the first person to check in for an upgrade, if necessary. Other factors do come in to play, for instance their evaluation of the passenger's commercial importance. But, all things being equal, being among the first checked in with a seat assignment is the best place to be.