They serve as an explanation for why you posted.
Bump signifies your intent to place the story at the top of the current posts list. Any reply will accomplish this but sometimes we have nothing to say but feel the story deserves more read time on the board.
BTTT is the same thing. It stands for "bump to the top".
ping is used when your intent is to call the thread to the attention of someone. When you reply on the thread, you remove the name that comes up in the "To" box and type the name of the freeper you wish to call to the thread. The thread will now show up in their self search function.
There is a thread for freeper speak but I don't have the link to it.