The library's note
Start with what "change" is. A cup of coffee is actually hot and potentially cold; when it cools, that potential is made actual. Aristotle's basic claim is that a potential cannot actualize itself — the coffee does not cool itself; the cold air does. So whatever is changing is being changed by something else that is already actual.
Everything then turns on what kind of causal chain is in play, because there are two, and they behave very differently. The first Aquinas calls accidental (per accidens). A father begets a son, who grows up and begets a son of his own. Here each cause, once it has done its work, is no longer needed: the grandfather can die and the grandson is born all the same; the son becomes a cause in his own right. The links do not depend on the earlier ones still operating. A chain like this, Aquinas freely grants, could in principle run back forever — he does not think reason alone can prove the world had a beginning.
The argument depends on the other kind, which Aquinas calls essential (per se). Picture a hand pushing a stick that pushes a stone. The stick moves the stone only because the hand is moving the stick, right now — the stick has no power to push on its own; it merely passes along power it is receiving this instant. A choir holding a note only while the conductor beats time, or a chandelier hung from a chain whose every link is held up by the one above, is the same: each member is borrowing its activity, at this moment, from the one before it. The defining mark of such a chain is simple — the instant the first cause stops, everything stops. The stone halts the moment the hand does; the note dies the moment the conductor's hand falls.
A chain like that cannot run back forever, because if every link were only passing along borrowed power — if there were no first member actually supplying it — there would be no power in the chain at all, and nothing would move. Yet things are moving. So an essentially ordered chain must rest on a first cause that is not itself being moved by another: something with no unrealized potential to be actualized, "purely actual." And because such a cause has no potential left to be actualized, there is nothing prior that could actualize it — which is the reply to "then what changes God?" That first, unchanging cause is what Aristotle and Aquinas call God.
Written for this library — not a quoted source. It reports how the premise is argued and answered; the philosophers' own words are above.