A contralateral movement pertains to exercising muscles on opposite sides of the body from one another. To give you a better idea, in the figure above the man is doing a core movement called opposites. It is a contralateral movement because he is extending his left arm and his right leg simultaneously. This involves appendages on opposite sides of the body.
Physical therapists and athletic trainers who help people recover from injuries sometimes use contralateral exercise during rehab. Fore example, to rehabilitate a knee injury the healthy leg can be strengthened. Studies have shown that one side of the body being strengthened can have positive effects on the opposite side.