Most of what I know about Kaluza-Klein Theory comes from a book I read a while back by Brian Greene called "The Elegant Universe". What he said was that Kaluza had figured out a way to incorporate a fifth dimension of space-time to the equations of relativity and out popped electromagnetism. Although he wasn't really specific, I was enthralled by this idea and figured that it must be the key to the Unified Field Theory (until I realized it was discredited).
Can someone explain this theory in greater detail and why it failed?
(I am not an expert in math, so preferably words over numbers, unless absolutely necessary)