The starter motor is a powerful electric motor that provides the initial impulse to turn over the engine to start it. It requires a very high current to crank the engine, which is why it is attached to the battery with large cables. When you turn the ignition key to the start position the battery voltage goes through a circuit to energise the starter motor.
When the starter motor doesn't turn fast enough it is either a problem with the motor itself or the battery has run down.