What does "$\text{Hom}(\space, G)$takes values in Groups" mean? From Rotman's Algebraic Topology:

When we say that $\text{Hom}(\space , G)$ takes values in Groups, then it follows, of
  course, that $\text{Hom}(X, G)$ is a group for every object $X$ and $g^*$ is a homomorphism
  for every morphism $g$; a similar remark holds if $\text{Hom}(G,\space )$ takes
  values in Groups.

What does "$\text{Hom}(, G)$takes values in Groups" mean?  The text seems to indicate that $\text{Hom}(X, G)$ is a group for every object $X$ follows from assuming this, but I don't know what this means.
Anyone know what this means? 

It is stronger than saying that $\text{Hom}(X, G)$ is a group for every $X$; it is also saying that this group structure is natural in $X$. 
More formally, for any object $G$ the functor $\text{Hom}(-, G)$ takes values in sets, meaning that it is a functor $C^{op} \to \text{Set}$. What it means for this functor to take values in groups is that it factors through a functor $C^{op} \to \text{Grp}$. And in fact you can show that such a factorization is equivalent to a choice of group object structure on $G$. 
