When a wire carrying a current is placed in the magnetic field of a magnet, the wire experiences a force. This is called the motor effect. If there is no current, there is no force on the wire. If the current is reversed, the force on the wire is reversed.
Forces always come in pairs. The magnet exerts a force on the wire, so the wire exerts an equal and opposite force on the magnet. The two forces are the same size but act in opposite directions, and one acts on the wire while the other acts on the magnet.
You can show this by placing a magnet on a balance and holding a wire carrying a current in the field of the magnet. If the wire is pushed up, the magnet is pushed down and the reading on the balance changes.