It's shock on the drivetrain mostly. You have a certain level of grip to overcome at the tire, so you through a bunch of power through the clutch, down to the tire to crack it loose, which is going to put wear on your tires and clutch potentially, depending on how the burnout occurred.
If you shift into higher gears before the tire stops spinning, or keep it hammered on and switch gears, you are going to cause clutch and synchro wear. Trying to keep the momentum of the wheel(s) spinning involves being fast and throwing it into the next gear. Which isn't really a set of parameters the drivetrain was built for. Not to mention the potential of wheel hop, which can be damaging.
I'd like to go more in depth on it, but I have to get to work. So this mediocre answer should get the ball rolling. Lol