What is the basic purpose and principals of a DC motor?

The basic purpose of a DC motor is the conversion of electrical energy (direct current) to mechanical energy. It operates on the principle that when a current carrying conductor is placed in a magnetic field, the conductor experiences a mechanical force.
Fleming's left-hand rule is very useful here. If we stretch the first finger, second finger and thumb of our left-hand perpendicular to each other; and we assume that the first finger represents the direction of the magnetic field, the second finger represents the direction of the current, then the thumb will represent the direction of the mechanical force experienced by the current carrying conductor.
The magnitude of the mechanical force is given as the product of magnetic flux density, current and the length of the conductor within the magnetic field.
From an operational perspective, a DC motor contains a permanent magnet or an electromagnet. The armature windings, connected to a DC source, are placed between the north and south poles of the magnet. As per the principle mentioned above, the armature windings experience a mechanical force. Unidirectional torque is achieved by making a segmented commutator.
Hope this helps.