When two equal and opposite forces are applied on a body at the center of mass of the body, then there is no net force on the body. If the body is moving at a uniform speed, it will continue to be in the state of uniform speed. If the body is at rest, then it will continue to be at rest. This is according to the law of inertia or Newtons' first law. If the body is already in a state of uniform motion with uniform velocity, then the body will have displacements in time.
If the two forces are acting at different points other than through the center of mass, then there will be a torque, the body will rotate. If the body is already at rest then it will rotate only but not translate and hence there is no translational displacement. But there is angular displacement (angle).