This seems like such a simple question, I had to tune in to see how folks were beating it to death, as we often do.
@Mustangman, I originally had the same thoughts as you, but as soon as I got to the part where someone explained that more fuel can be dumped (or injected) into the cylinders even though the RPMs don’t change, I understood where my thinking was wrong.
With automatic transmissions being the new norm, we’re used to seeing the RPMs jump up when the transmission downshifts, but if you have a car with a manual transmission, you can actually test this, even if you don’t have a tachometer. Just listen to your engine at different speeds. Get up to speed, put it in top gear, and floor it. The RPMs don’t change until the speed changes. You can hear it.