NS - permanent magnet
ABCD - coil wire
B₁ B₂ - carbon brushes
S₁ S₂ - split ring

Flemings left hand rule:
Flemings left hand rule states that while stretching the three fingers of left hand in perpendicular manner with each other, if the direction of the current is denoted by  the middle finger of the left hand and the second finger is for direction of the magnetic field, then the thumb of the left hand denotes the direction of the force or movement of the conductor.

First law: Whenever there is a change in magnetic flux linked with a coil, an electric current is induced. The induced potential difference lasts so long as there is a change in the magnetic flux linked with the coil.
Second law: The magnitude of the induced current is directly proportional to the rate of change of magnetic flux linked with the coil

Explanation:
When the coil is rotated, the magnetic flux linked with the coil changes. This change in magnetic flux will lead to generation of induced current. The direction of the induced current, as given by Fleming's Right Hand Rule, is along ABCD in the coil and in the outer circuit it flows from B₂ to B₁. During the second half of rotation, the direction of current is along DCBA in the coil and in the outer circuit it flows from B₁ to B₂. As the rotation of the coil continues, the induced current in the external circuit is changing its direction for every half a rotation of the coil.

Principle: An electric motor works on the principle that a current carrying conductor placed in a magnetic field experiences a force. The direction of force is given by Fleming's left hand rule.
Construction: An electric motor consists of the following main parts.
Armature: It is a rectangular coil ABCD having a large number of turns of this insulated copper wire wound over a soft iron core. The armature is placed between the poles of the field magnet and it can be rotated about an axis perpendicular to the magnetic field lines.
Split rings (commutators ): It consists of a cylindrical metal ring split into two halves S1 & S2. As the coil rotates, the split rings also rotate about the same axis of rotation. The function of the split ring is to reverse the direction of current in the coil after every half rotation. Carbon brushes: Two graphite or flexible metal rods maintain a sliding contact with split rings S1 and S2 alternately.
Battery: A battery of few cells is connected to the brushes. The current from the battery flows to the armature coil through the brushes and the split rings with split rings S1 and S2 alternately battery flows to the armature coil through the brushes and the split rings.
Working: A simple coil is placed inside two poles of a magnet. Now look at the current carrying conductor segment AB. The direction of the current is towards B, whereas in the conductor segment CD the direction is opposite. As the current is flowing in opposite directions in the segments AB and CD, the direction of the motion of the segments would be in opposite directions according to Fleming's left hand rule. When two ends of the coil experience force in opposite direction, they rotate. If the current flow is along the line ABCD, then the coil will rotate in clockwise direction first and then in anticlockwise direction. If we want to make the coil rotate in anyone direction, say clockwise, then the direction of the current should be along ABCD in the first half of the rotation and along DCBA in the second half of the rotation. When the gap in the split ring commutator is aligned with terminals X and Y there is no flow of current in the coil. But, as the coil is moving, it continues to move forward bringing one of the split ring commutator in contact with the carbon brushes X and Y. The reversing of the current is repeated at each half rotation, giving rise to a continuous rotation of the coil.