[Haskell-beginners] map type explanation

I'm looking at this ghci> :type map map :: (a -> b) -> [a] -> [b] and wondering what the (a -> b) part is about. map takes a function and applies it to an incoming list. Good. Understood. I'm guessing that the whole Haskell type declaration idea is based on currying, and I do understand how the (a -> b) part "takes" an incoming list, [a] and produces the [b] output. Also, I don't understand a and b very well either. Typically, a is just a generic variable, then b is another generic variable not necessarily the same as a. But how are they being used in this type declaration? LB