When bees flit from flower to flower the nectar sticks to their legs. The phrase "bee's knees" means sweet and good, because the knees of the bee are where all the sweet, good stuff is collected.
That definition about moving around really fast is wrong.
Slang from the 1920s. Possibly a corruption of the word business. Another possibility is that it is derived from the expression, "be all end all" a.k.a. "B's and E's" which when said would sound like, "Bees-an-ees". Simply defined as the best, latest, and greatest. (Synonymous with other 1920s slang: The cat's pajamas and the cat's meow. A more current version would be The shit.).