Most tires are identified by an inscription like this one 180/70 Z 17. The first number "180" is the tire width in millimeters. The second one "70" is the height of the tire's wall in percentage of its width. "Z" is the speed rating, meaning how fast you are supposed to to drive before the tire blows in your face. Finally 17 is the wheel diameter in inches. Quite logical indeed.
 

You can only fit a limited ranges of tires sizes on a given rim size. While there is a "perfect fit", for instance 130mm wide tires are meant to be mounted on 3.0 inches wide rims, there is a small margin of tolerance. A 140mm tire will also fit on a 3.0 inches rim but its "profile" will be affected. By affected we mean that the profile of the tire will be squeezed to a sharper curve than the one intended by the manufacturer. A squeezed tire will offer less surface of contact with the pavement than intended and the sides of the tires will go unused. On a more positive note the handling of the bike may be improved, less surface contact and a sharped profile may mean a bike that "falls" more easily to the angle. A higher tire wall implies more tolerance to width difference between the rim and the tire. For example a 130/70 is meant to be mounted on 3.30 rim, but a 140/90 will also fit a 3.00 rim and eventually a 2.50. Finally consider the fact that front and rear tires do not have the same profile.
Obviously I am NOT suggesting to mess around with the constructor's recommendations, I am just providing some pointers that may help you understang how things work and what are you options when choosing new tires. Don't come whining if you fuck things up!

Now here is a little table I had a hard time finding when I was trying to figure out which rims would be the most appropriate to turn my TT-R250 into a super-motard. Some of the weird fit can be explained by the fact that off-road/dirt tires do not have the same profile as street tires and don't actually fit on the wheel the same way. Also tires from different manufacturers have different profiles and may be designed for a specific model or wheel size.
For more info on dirt bike wheels and tire check this article [cached] from MXTuner on Off-road.com