A division is a level of convention organization between the chairman and the areas. Modern Worldcons require divisions -- they are simply too large for a chairman to directly manage all of the area heads. By dividing the convention into 4-8 divisions, and appointing a division head to manage each of them, span of control issues are minimized.
Divisions are usually organized functionally -- a Services Division, an Exhibits Division, a Facilities Division, etc. -- but can also be organized according to the strengths of the person who will be the division head. For example, at Noreascon Three, one of the divisions was the WSFS and Art Show Division, which was created to cater to the strengths of George Flynn who headed it.
Creating divisions that are a group of functionally related areas makes sense only because locating areas which need to communicate more frequently in the save division may simplify communications. The argument has been seriously made, however, that communications is such an important issue in running Worldcons, and that the communication between the more closely-related areas is such a small part of the overall communication required, that it would be better to simply number the divisions 1 through 8 and assign areas randomly. While this would somewhat impede some kinds of communication, it would force communications issues to the surface and might well make for a better run Worldcon in spite of that. No one has yet had the guts to give this a try.
Smaller conventions rarely require a division structure, and when they have it is is more often because of politics (having division heads means more titles to hand out) or a love of organizational complexity, than of any real need.