Originally? It comes from the term copy pasta; something written that gets copied and pasted all over the internet. I cant think of any good examples at the moment, but often they are funny and weird, unless of course they are creepy and weird.
Now? If you ask Dead Palette (the man speaking on the video above) it is a kind of internet horror. It has to be believable, beyond the normal suspension of disbelief, a good creepy pasta needs to, on some level, be able to make you question if it is real or not. It doesnt mean it cant be somewhat supernatural, people are naive, after all.
Colloquially its a scary story you find on the internet.