The pity puff is the last toke of a joint. It is presented to the next person in the circle as a consolation offer. Usually it is the least tasteful part of the joint and also the hottest part to smoke. It is therefore offered as a "pity" toke, or "puff".
"There were too many people smoking on one joint, all I got was the pity puff."
And dying in yo' bed many years from now, would ya be willing ta trade all da days from dis here day ta dat fo' one chance, just one chance, ta come back here as young men an' tell our enemies dat dey may take our lives but dey will never take our freedom ... YUB NUB!