The transmitter flashes the LED very rapidly. This is to increase it's brightness by driving it at high(ish) current but for short periods so it doesn't overheat.
The receiver picks up the flashes in the photodiode as a tiny voltage change and amplifies it so the signal is bigger in the 741 op-amp. The amplified signal is then converted to DC in a voltage doubling recifier made from the two 1N4148 diodes and the two 2u2 capacitors. The DC biases the transistor into conduction which lets current through the relay coil and the LED across it. The relay is the switch that turns the light on or off.
It's a simple circuit and prone to false triggering from other flashing light sources such as fluorescent tubes and IR remote controls. A better design would filter the signal so only the frequency of flashes from the transmitter were allowed to reach the rectifier diodes.
Brian.