They allow you to run a bigger tire on certain frames. A 38mm tire is more comfortable than a 28mm tire.

I like a wider tire because I ride on the bad roads around here. I find them better on dirt and gravel roads also.

A 650b rim is smaller, and might lower the bottom bracket. For example, The radius of a 650b x 38 Col de la Vie tire is about 10mm smaller than a700x32 Pasela, and the bottom bracket is 10mm lower. However the outside diameter of the Col de la Vie tire is about the same as some 700cx23 tires, so there is no lowering of the bb.

The choice of tires is limited, but I am satisfied with The Col de la Vies and the Soma B-lines.

The pros and cons have been discussed on the C&V forum; there is some more information on the Rivendell site, and on the internet -bob, and 650b groups on Google.