You'll find some ELI5 answers here: https://steemit.com/faq.html#What_are_Steem_witnesses

There's no mining on Steem, but yes, it's a replacement for it. Essentially instead of solving difficult math problems, the community votes for who should run nodes to maintain consensus.

It's an election, the more votes the witnesses receive in terms of Steem Power of the voters, the more blocks they secure.

You don't get any benefits, but by voting for witnesses you trust, you indirectly make Steem a better place. Of course, large Steem Power holders have a significant effect on the political landscape of Steem.