In a Permanent Magnet motor a coil of wire (called the armature) is arranged in the magnetic field of a permanent magnet in such a way that it rotates when a current is passed through it. Now, when a coil of wire is moving in a magnetic field a voltage is induced in the coil - so the current (which is caused by applying a voltage to the coil) causes the armature to rotate and so generate a voltage. It is the nature of cause and effect in physics that the effect tends to cancel the cause, so the induced voltage tends to cancel out the applied voltage (indeed were the effects to add, we should have a perpetual motion machine!).
Voltage is electrical pressure. Current is electrical flow. Pressure tends to cause movement, or flow so an electrical pressure is a force which moves electricity - or an 'electromotive force' (EMF). The induced voltage caused by the armature's movement is a 'back EMF' - 'back' because it tends to cancel out the applied voltage so that the actual voltage (pressure) across the armature is the difference between the applied voltage and the back EMF.