Simple Terms: 650b in simple terms is the size between your standard 26″ and the newer 29″.

Detailed Terms: 650b can be viewed in a more scientific standpoint or in a more “Sheldon Brown” way where everything is taking apart.

650b is how the French size tires. (The French have to be different of course!) This is where I will leave it to Sheldon to explain:

In the French sizing system, tires are designated by a three digit number and a letter. The number is the nominal outside diameter of the tire the rim was originally designed for. The letter indicates the width of the tire: “A” was originally a narrow tire about 30 mm, so the 650A rim is pretty large, 590 mm. If you add the top and bottom 30 mm tire thickness to 590, you wind up with the 650 mm tire diameter.

The 650C size was originally intended for a quite wide tire, about 40 mm wide. top and bottom 40 mm tire plus the 571 mm rim size again bring you to a 650 mm outside diameter, even though the rim was smaller.

With time, however evolutionary processes have led to different widths of tires being applied to the rims than the originals, so the nominal 650 mm designation is now more theoretical than practical.

• 590 mm 650A is the size used on the classic English 3-speed . There’s nothing theoretically wrong with this size, but in practice, the selection of tires and rims available for it is pretty scanty these days.
• 571 mm 650C was originally a wide, ballon tire size, used on many older Schwinn cruisers. These days, however, it is mainly seen on triathlon bikes and time-trial machines. Available tires and rims are mostly very narrow models, intended for competition use.
• 584 mm 650B is the focus of this article. This size, also known as “26 x 1 1/2″ is most popular in France where it was the traditional size for loaded touring bikes and tandems, as well as general utility bikes.

Breaking it down to millimeters : The 650b is 584mm ISO ( International Organization for Standardization) or ETRO ( European Tyre and Rim Technical Organization.) Compared to a 26 at 559mm and the 29 at 622mm.

Link & Learn: Links that have educated me about the 650b and where I pulled much of this informaion from.

Sheldon Brown - Page on 650b; Page on tire sizing;
650b Freewebs - My original resource