Interference is a two minute minor penalty in the game of hockey. Almost anytime a player impedes a player on the opposing team somehow, and the offended player does not have the puck and is not involved in the play or is in the process of obtaining the puck or making a play, interference is called. Interference is not called, usually, when the impediment is actually some other penalty, such as high sticking, tripping, roughing, spearing, etc. During the two minute penalty the offending team is shorthanded and the other has a power play. See those nodes for more information.
The problem with interference is, at least in the opinions of most rabid hockey fans, it is not clearly defined or consistently called. Sometimes it appears to be handed out too often or easily, and sometimes not enough. It has become an issue in the late 90's-early 21st century when it was decided that this would be called more often in an effort to reduce interference with talented, goal-scoring players and thus promote more offense. It seems really unfair when this is called when a player is hit cleanly right after he has given up the puck. Technically, he doesn't have the puck, but the hitting player was just finishing a check, as they like to say, meaning he was going in for a hit when he saw that that player had the puck and he wasn't going to stop. Calling interference in this situation draws boos because hockey fans feel that it's harming the physical aspect of the game, something most fans hold in high regard, and making players more skittish about hitting each other.
At one point in time in the late 90's there was a crease interference rule that basically said that any goal scored while a player was in the goaltender's crease area, or any part of that player (foot, hand, or even a toe - yes, a toe), the goal was disallowed. This was to reduce danger to goalies of getting hit in attempts to score. In the 1999 Stanley Cup Finals, then-Dallas Star Brett Hull scored the cup-winning goal on Dominik Hasek in triple overtime in Game Six vs. the Buffalo Sabres (the game was in Buffalo). The goal was tainted because Hull's foot was in the crease and it should have been disallowed, but it was not. Buffalo fans are still sore about it.
That rule disappeared before the 1999-2000 season.
Thanks to avalyn for pointing out the now-defunct goalie interference rule.