Very briefly put: the STEEM currency has a fixed inflation rate. Every day there are around 43.000 new STEEM printed, and this amount is called "the reward pool". Out of it, around 75% goes to authors (the rest goes to witnesses, those who are maintaining witness nodes, which are validating transactions).

The more Steem Power you have, the bigger the amount you "draw" from the reward pool when you vote. That's from where you get money when you get votes: the voter, based on his influence, "draws" from the reward pool.

As for which pushes the price up or down, the discussion is way more complex than that. It's not only the value of the website which is taken into account, but also the blockchain characteristics (no transaction fees, very small transaction times, fungibility, etc). So the economics behind Steem are quite complex.