Closing the switch S for the simple relay causes a current to flow in the coil. This generates a magnetic field which magnetizes the soft iron core. Magnetism is induced in the pivot, also made of soft iron, which is then attracted to the soft iron core. This causes the pivot to swing back and enables the insulated wire to form a circuit with the motor, which can then start.
Similarly closing the switch T for the reed relay enables a current to flow in the coil. A magnetic field is generated, causing the contacts inside the coil to attract each other, forming a circuit. The motor can then start. The relay coil performs essentially the same function as the simple relay, but has less moving parts, so is more reliable and faster.