You normally have 6 players on each team in an ice hockey game (5 skaters and the goalie). If a player commits a penalty (e.g. tripping another player, holding, hooking), then he has to sit in the "penalty box" for a few minutes. While he is being penalized, his team must play with only 5 players, while the other team continues to have 6 players. This creates extra scoring opportunities for the team which has the "man advantage."
If another penalty is assessed before the first one expires, it is possible for a team to have a "2 man advantage."