In the original Halo, my friends and I would have what are essentially warthog wars. Each person gets into a warthog. You drive your opponent. If you have passengers, no one shoots. The point is to ram each other and try to flip the other into the air. Hopefully, when they land, they land in such a way that they fall out of the warthog. Now your job is to run them over before they get back in. They try to flip the warthog and get back in as quick as possible. If the unflipped person runs over the guy who fell out of his warthog, that kill is called a "bedurnk."
That's how it was with my friends. Since I helped create the term, and the guy who co-coined it already had a suitable gaming nickname (EmTea, his initials spelled phoenetically, Matthew Thomas (first and middle)) and my nickname irl is my last name and I don't want to give that out on a whim, bedurnk has been my gaming name ever since. Due to an error in registering for the Red vs. Blue forums, I changed it to b3durnk, which has stuck ever since.
I find the biggest problem with this term (which we didn't realize until I started going online with it often), is that people call it "be drunk" when reading it quickly. Thus I have to specify to any new group of players, such as I did in my app here, that is not the case and I do not endorse the act of drinking alcohol. :x
Complicated, no? But hey, I like complicated.