When I was a kid, we didn't have fancy things like cut-and-paste on computers. (I am young enough that I did have my own computer as a kid, so that means I'm less than 40, right?)
I remember when programs like WordStar and WordPerfect arived and let you copy and cut text from one place in a document and paste it somewhere else. It's amazing to think this was actually a new thing!
Then came Windows 3.x, with its fancy GUI. (OK, strictly speaking the Mac was there first, but I never played with a Mac much...) Now you could cut and paste between different programs! There was this thing called the clipboard, and a desktop for you to put all your files, so you could easily find them (Hahaha, that was a great idea -not!)
Things have stayed fairly much the same since then - computers are faster and Windows has gone through some changes in terms of look and feel, but the clipboard has pretty much remained as-is. If you were really bleeding-edge you could get a program to duplicate your clipboard across machines - useful when you are writing code or doing email on machine A and debugging on machine B.
Now, in the always-online age, it seems logical to use the Internet as your clipboard, and we now have various websites devoted to this (called Pastebins). Sites like Pastebin.com and Paste2.org are all the rage. Initially created to allow "collaborative debugging", it didn't take long for 1337 H4x0rs to start using them to share stolen passwords, credit card numbers, and exploits.
PS: Remember when collaborative debugging was done over email, newsgroups, or web forums?