I know that not getting enough sleep when you're trying to build muscle will "set you back". But what exactly does that mean? Does it mean that you'll actually lose muscle, or does it mean that it'll just take longer for your body to heal the small tears in your muscles from the previous workout? I try to get enough sleep (8-10 hours), but sometimes I can only manage 6 or 7 hours. I really don't want to spend hours at the gym just to lose muscle!

You wont lose muscle. And sometimes getting 'only' 6 to 7 is NOT a problem. Setting yourself back would be getting 2-4 hours sleep a night. You wont lose muscle anyway, you'll only hinder your progress as our muscles grow from proper rest/sleep...and youre getting proper sleep, so dont worry about it.