fmap transforms a “normal” function (g :: a -> b) into one which operates over containers/contexts (fmap g :: f a -> f b). This transformation is often referred to as a lift; fmap “lifts” a function from the “normal world” into the “f world”.
–Wikipedia “In mathematics, a functor is a type of mapping between categories, which is applied in category theory. Functors can be thought of as homomorphisms between categories”