Hockey is actually a pretty simple game, once you get used to it. But there are still some terms that are a bit unusual that aren't so easy to figure out.
If you've watched an NHL game before, then you know that hockey's got some odd terminology. Some things are more obvious than others. Here are what some of the terms mean.
Minor penalty - The standard two-minute penalty. A double minor is what it says: two minor penalties, back-to-back. See NHL Rule 16, Table 2, for a list of minor penalties. See NHL Rule 18, Table 4, for penalties that are automatically a double minor penalty.
Bench minor penalty - A two minute penalty that is called on the bench for breaking the rules. See NHL Rule 17, Table 3, for a list of bench minor penalties.
Major penalty - A five-minute penalty, most often used for fighting. Hence the phrase, "five for fighting". There are a whole bunch of major penalties that don't get called as often as fighting, however. See NHL Rule 20, Table 5.
Misconduct penalty - A 10-minute penalty, often for unsportsmanlike conduct, but does not create a short-handed situation for his team. Other penalties awarded along with a 10-minute misconduct will result in a power play for the other team. See NHL Rule 22, Table 9.
Game misconduct penalty - An automatic ejection from a game, usually for unsportsmanlike behavior. Supplementary off-ice discipline hearing is scheduled a day or two following the game in which the incident occurred, which can result in suspensions and fines. This is often awarded with a major penalty. Three game misconducts in a season can result in an automatic one-game suspension after the third incident. See NHL Rule 23, Table 10, for penalties that can also be assessed as a game misconduct penalty.
Match penalty - An automatic ejection from a game, usually for intent to injure another player, and often requiring that other player to be injured. Supplementary off-ice discipline hearing is scheduled a day or two following the game in which the incident occurred, which can result in suspensions and fines. This if often awarded with a major penalty. Match penalties, however, are rarely called in the NHL. See NHL Rule 21, Table 8, for penalties that can also be assessed as a match penalty.
Line change - A forward line on the bench changes places with another forward line on the ice - or vice versa. Can be during a break in play, but can also happen during the flow of the game as it's going. Defensemen can go for a line change - that is, get off the ice so someone else can take his place - but a "line" is considered three forwards while defensemen are in "pairs". See NHL Rule 82.
Changing on the fly - A line change while the puck is in play.
Power play / penalty kill / special teams - One team has more players than the other team does, due to a penalty. If it's your team with one more guy, then it's a power play. If it's your team that took a penalty and has one fewer guy, then it's a penalty kill. Both are considered special teams, as the strategies are different in these situations from regular game play. Also, some guys will play on the power play and not the penalty kill, and vice versa, so there are players whose talents are better suited for one than the other.
The crease - The blue paint in front of the goalie net. It is also the area between the penalty boxes in front of the scorer's table where the referees call penalties and talk to their superiors on questionable calls and play reviews. I have no idea where the name came from, but it sometimes makes for entertaining hockey calls. See NHL Rule 1.7.
Icing - If, when a player passes a puck, it crosses more than half of the length of the rink and a teammate touches it, the play is called dead and the puck will be dropped inside that team's blue line. If a player from the opposing team touches it, then the puck remains in play. See NHL Rule 81.
Offsides - The puck must fully cross the blue line of the offensive zone before any attacking player if fully over the line. That is, the zone where a team is shooting on the opposite goalie. (The zone with a team's own goalie is the defensive zone up to the blue line in front of that goalie.) A player may have a skate on the blue line and then bring the puck over. If the puck is in the offensive zone, but crossed the blue line, then no attacking players can bring the puck back over the blue line again until all of the players on his team fully clear the zone. It's acceptable for the puck to be on the blue line, however. See NHL Rule 83.