Functoris the class of types
f :: * -> *which can be covariantly mapped over. Mapping a function over a data structure applies the function to all the elements of the structure without changing the structure itself.
A Functor can be thought of as a container for some value, or a computation context. Examples are
Maybe a or
[a]. The Typeclassopedia article has a good write-up of the concepts behind Functors.
To be considered a real Functor, an instance has to respect the 2 following laws:
fmap id == id
fmap (f . g) = (fmap f) . (fmap g)