The first N means the function f takes arguments from the set N, that is the set of natural numbers ie: the positive whole numbers {1, 2, 3, 4,...}. This is the domain.
The second N means the function f returns answers that are taken from N, the same set of natural numbers. This is the codomain. We could equally define our codomain to be Z, that is the set of integers ie: the set of whole numbers, either positive, negative or zero. Remember not every number in the codomain has to be the answer f returns for some number in the domain.
The image of this particular function f is the set of values in the codomain that f returns as answers when f is passed some (valid) argument from the domain.
So the image (which is I think what you are asking about) is {1, 4, 9, 16,...}