It means to draw level with, or to match an opponent. It presupposes that one side was behind before the act that leads to the equalization.
In your example it could mean that black will recapture a pawn or piece, or will have a evenly matched board position after a specific move.
Remember, that white has an advantage, simply by virtue of moving first. At grandmaster level, for black to reach a position that nullifies that advantage and makes the game equal, instead of white being ahead as he is on move 1, is an achievement worth shooting for. That's why they go on and on about black being able to equalize in certain positions.
thanks a lot guys
White starts first, so that means it has the initiative, which is a plus in chess. After some moves, white can lose its initiative, so balck is equal. Enter the game position into a chess engine and the evaluation should show nearly 0 (i.e. white and black are even).
I have been going through a lot of annotated chess games and I often come across phrases like "black can equalise after a particular move" and I dont know what this means. Pls help.