Wikipedia says it better than I can!
Handle bar diameter
Both quill and threadless stems come in a variety of bicycle handlebar clamp diameters. The ISO standard for the clamping area of a handlebar is 25.4 mm (1 inch), which is used on mountain bikes and many Japanese-made road handlebars. However, the Italian unofficial standard is 26.0 mm, which is the most common clamp size for road bars. There are also intermediate sizes such as 25.8 mm to try to achieve compatibility with either an ISO or Italian stem, and the old Cinelli-specific size of 26.4 mm. In practice, many modern stems with removable faceplates allow for slight differences in handlebar clamp diameter, but the older type of stem with a single pinch bolt must be accurately matched. In the days of quill stems, a road stem was clearly identifiable from its "7" shape, but nowadays it can be hard to tell the difference between a "road" (26.0 mm) and "MTB" (25.4 mm) stem. Manufacturers frequently omit the clamp size from advertising or packaging.
BMX bikes usually have a 22.2 mm diameter clamp size.
A more recent standard is a 31.8 mm (1.25") clamp for both MTB and road bars. This is rapidly taking over from the previous mix of sizes, although other accessories such as some light or computer brackets may also need to be oversized to fit the thicker bars. Standard brake levers can be used as it is only the stem clamp central section that is oversized. Shims are available to fit a 31.8 mm stem to either a 25.4 mm or 26.0 mm bar, so many new models of stems are oversize-only.