The situation when a team has the maximum available number of skaters allowed on the ice (not including the goaltender). In the NHL, the game is played at five on five, so a team at full strength has five skaters on the ice.
The phrase "back at full strength" is used often when a team has killed off a penalty and their penalized player(s) is/are back on the ice, and the team is now playing with five skaters. Barring any major brawls or incidents happening during a game, an NHL game is played at full strength or at five on five for the most part. It is crucial then for a team to play well during five on five situations.
Full strength and even strength are often confused for each other, but the main difference is that even strength is when both teams have the same number of players on the ice, while full strength is always a five-on-five situation (with both goaltenders still in their nets). For example, during a four-on-four situation, teams are at even strength but not at full strength because each team has taken a penalty.