In the game of cricket, a declaration occurs when the captain of the batting team decides that although the team's innings has not yet finished, it would be advantageous to "declare" the innings over in order to have more time to bowl the other team out.
This oddity arises because of the limiting factor of time in cricket. To win a test match the opposing team must be bowled out twice, however there is a limited amount of time (5 days) in which to do this. If the captain of the batting team considers that the extra time to do this is more important than the extra runs foregone by declaring the innings over, then a declaration will be made.
A declaration not only gives the declaring team more time in which to bowl out the opposition, it also gives the opposition more time to score the runs needed to win the game. For this reason, a declaration is typically seen as an attacking move by a captain, as it increases the likelihood of a match resulting in a win rather than a draw. One traditional strategy is that by declaring early and giving your opponent a chance to score the required runs, you motivate them to play a risky attacking game that gives you a better chance of bowling them out.