(this is in reply to a now deleted post by Bioshock)
I added an explanation to my other post right about the same time you added your question to yours, but I'll explain it a bit better:
There isn't any one specific tool that leaves behind transparency. In GIMP, as long as your image has an alpha channel, anything like Delete, using an eraser, or moving something will leave behind transparency. (if you don't have an alpha channel, it tends to leave the BG color behind, like what Microsoft Paint does). If the image doesn't have an alpha channel, you can add one by going to Layer>>Transparency>>Add Alpha Channel.
By the way, forget my earlier suggestion about selecting it and pressing delete. Just use the Background Eraser tool instead
Oops, never mind, I got it confused. GIMP doesn't have a background eraser tool.