FeDeX_LaTeX said:
(at what rate, anyway? I can't understand how we'd figure out a 'rate'), ...
Well it's
distances that increase at a certain rate, largescale distances say between independent clusters of galaxies. I can't think of a object that I'd call a "thing" that actually "expands".
But distances change, and overall they certainly increase.
You asked about the overall rate of distance increase. The rate is currently that these largescale distances increase at a rate of about 1/140 percent every million years.
So how much increase depends on the size of distance. It sounds like a small percentage growth, like it wouldn't amount to very much. But for a very long distance, something like 1/140 of a percent can amount to quite a big addition.
=====================
You asked why,and and Torquil explained that this pattern of increasing distances got started around the time of "big bang" (which according to some models was a kind of bounce, not the beginning of time). There is a law that governs the dynamic change in geometry, and one consequence of the law
is that the pattern of increase will persist unless something slows it down or speeds it up.
Ordinary matter's attraction for other matter tends to slow it down, but as it happens there wasn't enough density of matter to stop the process. There are some technical details, like conjectured 'dark energy'. But even without 'darkenergy' distances would still be expanding right along at this time, according to the law (the equation that governs the evolution of geometry, distances etc.)
So there is no especially simple explanation for why. Except that the law, the equation that governs changing geometry says that it should keep on. The law is called the Einstein equation of General Relativity and the equation has been checked and rechecked with astronomical observations in every way that people could think of and it checks out very precisely. It says how much matter density we would have needed to stop the expansion by now, and we haven't got that amount, so it keeps on. (and somewhat more so now because of the 'dark energy' factor which also goes into the equation.)