As much as I know these words from Quran are about the will of a society. For example, Imagine a society that is ruled by a dictatorship and people want to get rid of it or make a revolution or something like that. According to these words, Allah won't change their condition (dictatorship) to any better condition itself while people stand by and do nothing. (Allah is able to do it, but Allah won't). But when (In this example) people stand up against dictatorship and really do things to get rid of it, then Allah changes the condition.
I'm not a professional at interpreting Quran so my example may have flaws, but I just wanted to give you the idea.
In brief, we should start the change from ourselves, not just sitting there and praying for it but doing nothing and expect Allah change things (like with some kind of magic).