Taking a bump is
professional wrestling terminology for taking a fall. In other words, if you, as a
wrestler, take a
dropkick in the face, you're supposed to go down. This is taking a bump. Some say that taking a bump more refers to a fall off a high place that looks dangerous, like jumping off a turnbuckle and missing your opponent. For the purposes of this node, I'm going to use my definition - any type of fall at all. Actually, I'm surprised that this hasn't been noded already.
Now, the pro wrestling mat doesn't have a great deal of give to it, and a wrestler could very easily harm himself if he's not careful. Taking a bump well is a key factor in how good of a wrestler a person is to become. A good bump is also a key factor in the longevity of a wrestler's career. Taking bad bumps can cause a fair amount of damage to the body.
It's essential to learn how to do it properly, or you could wind up hurting yourself, which wouldn't be any good.
It's not very complex. Simply put, you have to try to take the fall over as large a portion of your body as possible. When you fall, take the fall with the entirety of your back. It doesn't hurt too much; it's a bit jarring at first, but you'll get used to it as time progresses. Keep your arms out perpendicular to your legs - this helps in keeping your back nice and flat.
The only other thing to consider: do NOT hit your head. This takes practice. Try to keep your head a little bit forward. Don't keep it in a straight line with your back. It takes some practice, but you'll get the hang of it after banging your head off the mat a few times.
Wrestlers to watch and learn how to take a bump: Mick Foley, Chris Jericho, Sting.