In basketball, the phrase "strong side" refers to which side of the floor the ball is currently on. The strong side refers to either side of the court on a given possession, not the team itself. For example, if a player dribbles down the floor into the right-most corner, the right side of the floor will be considered the strong side. If the player then passes the ball to the left corner of the court, the left side becomes the strong side.
This phrase came from the need to describe areas of the floor in a fluid manner. It helps coaches and players to be able to refer to a side as the "strong side", because general directions like right or left change constantly depending on ball placement. Using the ball as the reference point is a much more effective means to establish position. The opposite of the strong side is the weak side, the side without the ball.