John green's notoriously unruly hair
The Puff refers to John Green's hair, and it's size levels are thought to directly correlate with John Green's stress level. It is mentioned in countless Vlogbrothers videos, especially those in which John Green's hair is severely unkempt.
Examples of the puff
THE PUFF IS SUCH A WELL KNOWN INSIDE JOKE THAT IT EVEN APPEARS ON CRASH COURSE, ANOTHER CHANNEL BY THE VLOGBROTHERS: