The witnesses are the people running the servers that process all the transactions for the blockchain. Every time someone posts, comments, upvotes, transfers coins, etc - all of that is getting processed and stored in the blockchain by the witnesses. In addition to the processing, they are also the elected leaders of the blockchain, and do a lot of other stuff for the betterment of the community.

When you vote for someone for witness, your vote stays with them unless/until you unvote for them. You can see who you are currently voting for here: https://steemit.com/~witnesses.