Sorry for the super newb question. I literally played my first game last Saturday.

According to the tutorial video, either your house or a character can receive power tokens. Seems like the power tokens stay on the house unless they're taken by an opponent, but what is the point of putting power tokens on characters? If the character is killed, are those power tokens lost forever?

The advantage for using characters is that (unless you're running the Brotherhood agenda), you cannot lose power tokens off of your characters during power challenges. But, that power is definitely fragile... targeted kill, Valar, return to hand effects... many things can make that power vanish (and yes, once a character leaves play, power tokens on the character are discarded).

That said, if those characters are gaining power because of Renown... then you're also gaining the benefit of a potentially accelerated win. Potentially.