On which part?

Using convection to circulate the water through the heater? Simple.
Water neither compresses nor expands, however it does change density. Water reaches its maximum density at about 4 deg C.
As the water is heated in the solar collector, it decreases in density. When it does so, the cooler water in the pool wants to displace it, since the cooler, more dense water wants to settle as low as possible, it will push the warmer, less dense water out of the way to do it. As long as the inlet to the heater is lower than the outlet from the heater, this will maintain a sustained flow.
The flow is as follows: The cooler water in the pool pushes into the lower inlet for the heater, where it is warmed up. As it warms, it decreases in density, and is displaced by more dense, cooler water. The faster the water warms up in the heater (the hoter the sun) the faster this flows.
The self-regulating part is this: When it cools off in the evening, you don't want the pool to cool off. If you leave water circulating through the heater, it will instead become a radiator, giving off heat from the pool into the air. As such, you want to stop this as much as possible. As soon as the heater is not actually heating the water inside it, the water will start to cool, becoming more dense, and wanting to flow backwards. (This is why we need the one-way valve) Since it can't, it just stays in the heater, which leaves the warm surface area being just that of the pool itself. Heat is transferred by surface area, and the heater is a way to increase the effective surface area when there is more heat energy available.
Of course, once it starts to fall below 4 degrees C at night, this whole thing stops working, but then your pool is in danger of freezing, and should be drained anyway.