Each ward is broken into divisions. There are currently 1,703 Divisions are sometimes called precincts. A division is the one of the smallest political units in the city (there are division-splits, which are smaller, but they are seldom used.) Each voter in the city is assigned to a division. It is customary to refer to your division first by the number of the ward in which you live, and then the actual division. For instance, I live in ward 55, division 19, or 55-19 for short.
The number of divisions changes over time. That is because a division is supposed to contain between 100 and 1,200 voters. As population changes, voters and elected officials may petition the courts to split a division (in the case of an increase in population) or consolidate divisions (in the case of shrinking population in an area.)
If you live in Philadelphia, and you want to find out the division in which you reside, go here. Just enter the information on the screen, and you will quickly find your division and your polling place. Please note that this screen provides a lot of information, so you may need to scroll down.