Lets look at an example of a Snake Draft:
Let's say you have 10 fantasy team owners in a snake draft where the 1st round of picks go in order starting from 1-10. Once the 10th team makes their draft pick, the order then reverses and will now go from 10-1 in the second round.
So the team that picks 10th, will have the very next pick and select 11th. This reverse order continues till you get to the team that selected 1st in the last round and now has the 20th pick in the second round. The process continues up and down (like going from the head of the snake to the tail and then back up) until all players have been drafted.