A Witness is basically a computer/server with a Steem account that verifies the transactions on the blockchain. It's similar to bitcoin mining. People want to be voted as a witness because you can make $$. It takes a LOT of votes to become a witness - I wouldn't worry about it too much right now.

Contests are created/run by other steem users. They can be a bit cheesy as most people only run these contests to get more followers/votes... that's why they always ask you to resteem/follow/vote etc. be weary of wasting your time with contests if it just looks like the person is looking for a payday