Hockey sense is your understanding of the game and capacity to apply it in game situations. Hockey sense develops with experience, but to different degrees for every player. Some will never be able to combine their understanding of the game with their in-game reactions, which is two seperate things. When the 2 are successfully merged, we refer to it as hockey sense or instincts.
More specifically, to me, hockey sense is your ability to read the play (at the ice level) in advance in order to react to it, whether be it in an offensive or defensive manner. To anticipate where your teammate is going to be or where you should position yourself to create a scoring opportunity. It's also being able to anticipate and intercept a pass from the other team, read the play as it happens and know what's going to happen next. Read the other player's game and outsmart him. In other words, read the game.
As a side note, Sheldon Souray said himself he developed his hockey sense during the time he was injured (year and a half) by watching a lot of hockey. He said it gave him a different perspective on things to watch the game from above, and anyone who one day played hockey, at any level, knows this is true. This is probably in part why he broke out last year.