A simple motor using Copper coil
Flemings left hand (motor) rule: -



If you pass current through a wire in a magnetic field then a force is produced. That force pushes one side of the coil outwards and, due to that current travelling in the opposite direction in the other coil side, it is attracted thus the coil turns. 
This happens because the current in the coil produces opposing and attracting magnetic fields.

However, it stops when aligned and this is not a motor as such. A DC motor requires a commutator to reverse the current at a certain mechanical angle so that the process repeats.

Picture source