What does he mean by "motion"?
Motion, in this case, is not limited to physical movement, like walking around a room. St. Thomas wrote that "motion is nothing else than the reduction of something from potentiality to actuality." By this he means that motion is what happens when any potential becomes actual.
- Wood has the potential to burn. When you touch a lit match to it, you move that wood from potentially burning to actually burning. That is "movement".
- Water has the potential to freeze. When you remove enough heat, the water changes. The water moves from being potential frozen ("able to be frozen") to actually frozen.
What does he mean by "nothing can be reduced from potentiality to actuality"?
By that he means that nothing changes spontaneously, without a cause. Wood doesn't go from "able to be burned" to "burned" on its own. There must be a match or ember or lightning strike. Something must make the change happen.
How about an example?
Domino #9 moves from potentially-falling to actually-falling when domino #8 hits it.
Domino #8 is moved from potentiality to actuality when actually-falling domino #7 hits it.
And so it goes, until we get back to domino #1. What about #1? That first domino has the potential to fall over just like the others. Dominos #2-10 all fall when they're hit by the domino ahead of them, but what about domino #1? What will move it from potentiality to actuality? What knocks it over?
We all know that the domino will not fall over on it's own. A finger may push it, or a cat's tail, or a gust of wind. The rock of the table as someone bumps it may tip it over. The point is that something or someone has to move it. Someone has to move it from potentially-falling to actually-falling.
An already-falling domino can make another domino fall over. Without an already-falling domino, you need an outside agent to get things moving. The sequence can't just go back forever, because there is always a first domino, and that first domino needs a push. There must be a "first mover", something or someone put in motion by nothing and no one else. This first mover we call God.
For more, watch Fr. Barron apply this idea in his video: Fr. Robert Barron on Scientism and God's Existence.
10-30-14 Update: Fr. Barron explains this further in Thomas Aquinas and the Argument from Motion.
Image courtesy of Enoch Lai. http://en.wikipedia.org/wiki/File:Toppledominos.jpg