A hockey team may have six players — typically three forwards, two on defence and one goaltender — on the ice at any given time. The rules allow for a team to temporarily bench its goalie in order to add an extra skater.
This is most common when a team is trailing by one goal late in the game and wants to even the score to force overtime. If play is in the opposing team's zone, the goaltender may await a signal from the coach to return to the bench so an additional offensive player can take the ice, theoretically increasing their scoring chances.
This happens while play is in progress and can be reversed quickly, provided that the number of on-ice players does not exceed six. I've seen a few games during which, seconds after making for the bench, the goaltender is directed back to the crease because the other team has gained possession of the puck so quickly that the extra attacker never left the bench.
Sometimes, if play is in the opposing team's zone, a team might pull its goalie while killing a penalty. This would bring its skater count back up to five.
Wikipedia notes that the first recorded use of an extra attacker came during a 1931 NHL playoff game between the Montreal Canadiens and the Boston Bruins. Despite pulling their goalie, the Bruins failed to tie the game and Montreal won 1-0. Bruins coach Art Ross is credited with inventing the technique.
"Pulling the goalie," as it's known, is typically an act of desperation. By doing it, a team risks the other team pushing back to their zone and only having an empty net to contend with. (That doesn't guarantee anything, though. To wit, watch Ales Hemsky of the Edmonton Oilers score on a breakaway after Patrik Stefan of the Dallas Stars missed the empty net in 2007.) You might call it the Hail Mary of hockey.
It's sometimes referred to as adding a "sixth attacker" or "extra attacker." And technically, "pulling the goalie" can also refer to the replacing of a goaltender who's been performing poorly with his or her backup. (In that case, it only refers to an explicit decision on the part of the coach to replace the goaltender. Sending the backup goaltender out because the starting goaltender has been injured is a whole other matter.)
(Oh, and it's also a euphemism.)
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