B-wings are heavy attack fighters, analogous in role to the Imperial Assault Gunboat (not in the films, I'll grant you, but I'm trying to give people a frame of reference. Ever play TIE fighter? Well why not??). They are only lopsided in their folded position. When their S-foils are open, they look completely different, rather like a cross with a blob on the top and a fat pile of engines. For a good picture, see http://starreacher99.tripod.com/picture/B-wing.html.
The B-wing name stands for blade wing (not bomber wing as often thought), referring to its dagger-like appearance. It was commissioned by the rebel alliance to combat the introduction of Nebulon-B frigates by the Empire. The Alliance at this time had no medium cruisers, could not spare the Mon Calimari cruisers from their more pressing front-line duties. Thus a heavy strike fighter, armed with both lasers and ion cannons, as well as a heavy warhead loadout, was designed. However, less favourable to the B-wing is its low speed (comparable to a Y-wing) and its low manouverability. On the other hand, its high levels of shielding and strong hull offset this disadvantage.