Before hard disks were common, computers generally had two floppy drives, one for running applications from and the other for saving your data. Since it's all more or less done from the hard disk now, you barely need one floppy drive, but B: is still reserved for a floppy drive.
If you start up a DOS prompt and switch to the B drive (type B: and press enter), it'll access the floppy drive, so A: and B: are now really the same place.
In ye olden days, the b drive was reserved for drives which took these floppies http://tinyurl.com/bvdqj
(different size and shape the the prevalent ones today)
... and great care had to be taken not to put the floppy in upside down, especially with a vertically mounted drive. The mnemonic I was taught was "label to loft, notch to knees"