Here I'll go over some more terminology and little more rule nuance.

For a refresher on the basics of the basic, please go to Hockey 101.

A few terms not discussed in Hockey 101:

Minor Penalty: This is a rules infraction where a player sits in the penalty box for up to two minutes.  If the other team scores prior to the two minutes, the penalty is over.

Major Penalty: This is a rules infraction where a player sits in the penalty box for 5 minutes.  There is no getting out early, no matter how many times the other team scores.

Even Strength: This is when both teams have the same number of players on the ice.

Power Play: This occurs when one team has at least a 1 person advantage due to the other team being penalized.

Shorthanded: This occurs when you're the team penalized.  The fewest number of skaters a team can have while shorthanded is 3, even if they are penalized again.

On to some rules that are slightly above the basics.

Stoppage in Play - A few reasons not discussed previously.

Hand Pass: This occurs when a player plays the puck with the hand in either the neutral zone or attacking zone.  Play is immediately blown dead if the offending team gains possession directly from the pass.  A face off occurs at the closest neutral zone face-off dot.

High Stick: This occurs when the puck is touched by a stick above the shoulders.  Play is immediately blown dead if the offending team gains possession after the puck touched by the high stick. A face off occurs at the closest neutral zone face-off dot.

More Terms Heard During Broadcasts

Delayed Penalty:  As you learned in Hockey 101, when a referee spots a rules infraction that warrants a penalty assessment, he raises an arm.  That arm does not lower until the penalty is assessed.  As long as the penalty has not been assessed, play is continued until the play is stopped when a goal is scored, the offending team gains possession, or any of the Stoppage in Play scenarios occur.  This is called a delayed penalty.

Delayed Offside:  If a puck is shot or passed into the attacking zone while an attacking player is already in the zone, the linesman will raise an arm.  It does not drop until the offending players "touch up" the blue line by touching it with a skate.  If the players touch up, play is continued.  If the player does not touch up and continues to try to play the puck, the linesman will call the offside.

Specific Areas of the Ice - See the illustration below.

Trapezoid - The goal tender is not permitted to play the puck below the goal line and outside of the trapezoid.

The Crease - The light blue area owned by the goaltender directly in front of the net.

Face-Off Circle - This is where face-offs occur.  The hash marks indicate where each team is supposed to have players lined up.  The attacking players line up on the hashes closes to the blue line and the defending players line up on the hashes closest to the goal line.

I hope this extra bit of information is useful to those who are just learning the game.