What is the biological process that causes muscles to grow?

I get that you do exercise and it damages the muscle tissue and then the body heals that damage (at least I think I get that) but then why does that cause muscles to increase in size over continued exercising sessions? If it's just repairing then I would have thought that it would just stay the same size but clearly it doesn't.

So what is the biological process (preferably in some step by step, if that's possible?) to how muscles continuously grow due to exercise?

And a side question, why are muscles our only tissue that we can train to grow passed their normal size?