/ as you know does classic division. // operator was added in Python 2.2 which does floor division, and with addition of this operator, you can use from __future__ import division to make / operator do true division.
a //= 3 is equivalent to a = a // 3.
So, here's the summary:
Python Version operator / operator //
-------------------------------------------------
2.1x and older classic Not Added
2.2 and newer classic floor
(without import)
2.2 and newer true floor
(with import)
