"e-Sports" is simply the short name for electronic sports. Just like football players play football together, e-Sports players play computer games against each other.
How much does a pro gamer make? It varies. The standard right now for a mid-to-high tier professional is $50,000 – $75,000 annually from salary only. Earnings from tournament winnings, sponsorships, and streaming are added and calculated based on how popular an individual player is.