What does Buddha mean with '' to not sacrifice one's life for another' (Dhp 166)?

Buddha did not believe in blood sacrifice, such as when Brahmans sacrificed animals to their gods or when the Hebrew patriarch Abraham was going to blood sacrifice his only son Issac.

There is no benefit in blood sacrifice. In Buddhism, to believe otherwise is superstition.

For example, many Jewish rabbis criticised Zionists in World War 2, accusing Zionists of deliberately sacrificing Jewish people for the sake of establishing Israel (refer to Ten questions to the Zionists by Rabbi Michael Dov Weissmandl.). Ben Gurion, a father of modern Israel, said:

If I knew that it was possible to save all the children of Germany by transporting them to England, and only half by transferring them to the Land of Israel, I would choose the latter, for before us lies not only the numbers of these children but the historical reckoning of the people of Israel. (Wiki-quote)

This shows what happens when blood sacrifice is considered to be a virtue. More here.

The above said, it is probably wrong to say Jesus was sacrificed in line with the Jewish tradition because there is actually no tradition of human blood sacrifice in Judaism (see link). When God asked Abraham to blood sacrifice Issac, this was only a test.

Therefore, when Jesus blood sacrificed himself, calling himself: 'The Lamb of God', & exhorted his disciples to "drink his blood", this sounds like the own idea of Jesus rather than a Jewish idea because Jews are forbidden from eating animal meat with blood in it, let alone human blood.

To most religious Jews, the idea of 'drinking blood' is alien & repulsive, which is at least one reason the vast majority of Jews for 2,000 years have rejected & even despised Jesus.

The Buddha cherished & valued all life, including animals. In Buddhism, it is a sin to kill living beings, including animals (unless absolutely necessary).

To not sacrifice one's life for another means to not harm oneself when helping others.

The Buddha said:

“Having gone around in all directions with the mind, There is surely no one found who is loved more than oneself.

“In the same way others each love themselves, Therefore one who cares for himself should not harm another.”

Ud 5.1.

I like this reference to the Dhammapada, because it includes the "story" behind each verse (note that it's the verse itself that should be treated as "Gospel", the story is commentary, sometimes allegorical).

So verse 166 can be found here: Dhammapada Verse 166 ... from which I take the following to be the essential message:

The Buddha then said to the bhikkhus,

"Bhikkhus, those who love and revere me should act like Attadattha. You are not paying me homage by just offering flowers, perfumes and incense and by coming to see me; you pay me homage only by practising the Dhamma I have taught you, i.e., the Lokuttara Dhamma."

In other words, the Buddha taught what he did to let each person to attain liberation. That's what the Buddha wants: for each person to attain liberation. So if you do something other than that, "for the sake of another's benefit", then you're missing the point of the Buddha's message.

Also, "not sacrifice your life" is a paraphrase or extrapolation of the verse, not a quote; actually it says,

Verse 166: For the sake of another's benefit, however great it may be, do not neglect one's own (moral) benefit. Clearly perceiving one's own benefit one should make every effort to attain it.

Also there are stories (fables) of the Buddha having sacrificed his own life, in past lives: for example, there's the story of the tigress (here's the short version and a longer version). Actually that story is told as admirable and perhaps even as a necessary step in the Bodhisattva's evolution towards birth as a Buddha. The Jataka tales are not entirely canonical though.

Also Buddhist are taught that generosity is a virtue (perhaps the first virtue; or maybe the second virtue after "harmlessness").

I'm not sure that generosity is seen as "sacrifice" though.

And literal "sacrifice" (perhaps using fire?) was a feature of the contemporary (pre- and post-Buddhist) religion: performed by priests of the "Brahmin" caste.

I think that the whole last chapter of the Dhammapada is on that topic: saying that what makes a person "holy" isn't sacrifice and so on, but self-restraint and so on.

There are some similar doctrine addressed to a Brahmin in the suttas also.