To trade pieces to quiet down the position, to eliminate the opponent's attacking potential, or to clarify the situation. The player with the better position is more likely to simplify than the player with the worse position.
To simplify is to change a mathematical expression to its simplest form. Also "perform the indicated operations" has the same purpose. (See also evaluate.) Examples: 3 + 4( -= 3 + 4 - -(-) xy)= (-= - 200