In the experiment shown below, a piece of cooper wire has been placed in a magnetic filed produced by three strong magnets. Copper is non-magnetic, so it is feels no force from the magnet.
However, with a current passing through it, there is a force on the wire. The force arises because the current produced its own magnetic filed, which acts on the poles of the magnet.
The force is increased if the current is increased, a stronger magnets are used or if the length of wire in the filed is increased. When we change the direction of the current in the circuit, the wire movers in opposite directions.