How does a muscle grow?
h2oiamwater is correct that overloading the muscle causes microscopic tears to the muscle and when these tears are repaired the muscle becomes stronger.
Lactic acid buildup is caused by anaerobic exercise and is not directly related to muscle growth.
pretty much i think (not 100% but along these lines) when you work out your muscles tear and produce lactic acid....and then they heal and build more muscle over that. Which is what makes them bigger after a while and is why your sore afterwards.