The first part of this principle is the idea that most things in the world have motion through growth, melting, running, burning etc. This motion is the reduction from potentiality to actuality. Potentiality is the potential something has to move and actuality is the concrete way something is in a given moment. For something to be in this actual state it must have had the potential to do so first. For example wood has the potential to burn for a piece of wood to burn it must first be changed by fire.
The next point Aquinas makes is that nothing can move itself. It is the same idea that Plato has, which states that everyone is a second mover. Nothing can move itself, for example, if I were to move a chair, the chair is the second mover. This continues into the next point that something must have moved me in order to move the chair.
The previous point suggests that for something to be moved it must have been moved by something else. Everything in the universe in order to move must have been moved by something else. Whatever is moved (changed), must be moved (changed), by another, which itself was moved (changed). If everything was a second mover there would be an infinite regress.
If the previous point was true and there was an infinite regress of movers and hence no subsequent movers it would not be possible for a prime mover, the cosmological argument believes this is false. Aquinas shows that infinite regress is impossible he does this using a reduction ad absurdum argument suggesting infinite regress is a