Part a) of Problem 2C.1 of Isaacs' Finite Group Theory reads
Show that every proper homomorphic image of an $N$-group is solvable.
What does "proper" mean here? Please note that I'm not asking for a solution to the problem, just a clarification of its statement, so I can work myself on it. (Incidentally, the definition of solvable group comes later in the book in Chapter 3, a rare oversight in Isaacs.)
A group $H$ is a homomorphic image of a group $G$ if there exists a surjective homomorphism $\phi:G\twoheadrightarrow H$. If $G$ is finite then $H$ is a proper homomorphic image if $G\not\cong H$; equivalently, if $\ker(\phi)$ is non-trivial.
As Isaac's book is about finite groups, this is the case here.
For infinite groups, these two conditions are not in general equivalent (see here) and so you should be careful using this term.