The real answer is that a functor is a type of mathematical object, and is "reified" by different languages in different ways. For example, suppose that you have a "container" object that stores a bunch of other objects of the same type. (For example, a set or array) Then, if your language had a method that let you 'map' over the container, so that you could call a method on each object in the container, then the container would be a functor.
In other words, a functor is a container with a method that lets you pass a method to its contained things.
Every language has its own way of doing this, and they sometimes conflate the usage. For example, C++ uses function pointers to represent the "passing in" of a method, and calls the function pointer a "functor." Delegates are just a handle on methods that you can pass in. You are using the terminology "incorrectly", just like C++ does.
Haskell gets it right. You declare that a type implements the functor interface, and then you get the mapping method.
Functions (like lambdas) are functors too, but it can be kind of hard to think of a function as a "container". In short, a function is a "container" around a return value, constructed in such a way that the return value (possibly) depends on the function's arguments.
