The blue lines are 60 feet from each end of the rink. The area between the two blue lines is the neutral zone. When you cross the blue line heading toward the other team goal, you are entering the offensive zone. The blue lines are critical for offside calls.
More in rules
Cross-checking
Shoving a player with your stick held in both hands. Cross-checking is when a player holds their stick with both hands and shoves it into another player. Imagine holding a broomstick horizontally and pushing someone with it. This penalty gets called a lot in front of the net where defensemen are trying to clear attackers out of the crease area. A little stick contact is usually allowed, but when a player uses their stick to deliver a forceful push, the referee calls it. It is a two-minute minor and can be a major if it causes injury.
Delay of game
Intentionally slowing down play. The most common version today is when a player in the defensive zone shoots the puck over the glass and out of play. That is an automatic two-minute penalty. Other examples include a goalie freezing the puck when there is no pressure, a player intentionally knocking the net off its pegs, or a team taking too long to set up for a faceoff. The rule exists to keep the game moving and prevent teams from stalling.
High-sticking
Hitting another player with your stick above the shoulders. High-sticking is when a player hits another player with their stick above the shoulders. If the high stick draws blood, it is a four-minute double minor instead of the normal two minutes. If a player scores by deflecting the puck with a high stick above the crossbar, the goal does not count. This happens a lot accidentally. A player will follow through on a shot or lose control of their stick, and the blade catches someone up high. Intentional or not, it is still a penalty.
Tripping
Causing another player to fall using your stick, knee, or foot. The most common version is when a player reaches out with their stick and clips the skates of the puck carrier, causing them to go down. It is a two-minute minor. If a player is on a breakaway and gets tripped from behind with no defenders between them and the goalie, the referee may award a penalty shot instead.