Why cuidado means "watch out!"/"caution!" when it is the past-participle form of cuidar?
The word seems to be a conjugation of "cuidar". If you are telling people to be careful (imperative), you would use the "cuida"/"cuide"/"cuiden" form. I can imagine "cuidate" being correct as well.
So, can somebody help me understand why "cuidado" is used? "cuidado" is the past-participle according to http://www.spanishdict.com/conjugate/cuidar
Good question. It is because "cuidado" (past participle of cuidar) comes from a Latin word meaning "thought", "considered". Then it evolved to "close attention" (English: care ;) ) and then into "worry" (English: care :) :) ). Then, "¡Cuidado!" is the short form for "¡Ten(ga) cuidado" (lit.: Have care! -> Be careful! / Be cautious!).
Today it is used like a normal noun that means "caution". ¡Cuidado con el perro! = Beware of dog!
I've always understood "cuidado" to be a noun, when it's not being used as a past participle. It turns out that is sort of true, but "cuidado" is fairly complicated: http://www.spanishdict.com/translate/cuidado.
It might help, though, to realize that "cuidado," when used in this sort of context, is best not understood as a verb.