Here's my best understanding so far:
A functor is a function that takes in a list of things and like a regular function, outputs a list of modified things...
So how is this different from a function?
To give a simpler example, we say a function, f, is monotone when for x<y, f(x)<f(y); that is, it preserves order. Every monotone function is obviously a function, but functions like x^2 are not monotone.
Basically a functor is a function which preserves some other properties. I wont go into detail as many have before me, but thats the gist.
For those who like me wanted to see the edge case for the non-monotonic function, if you do:
-2 < -1
-2 is in fact less than -1.
However:
(-2)^2 < (-1)^2 ==becomes==> 4 < 1
And 4 is obviously not less than 1.