Meaning of the notation $H \times -$ in category theory

Question

So I saw this notation in Saunders Mac Lane book on category theory. The original text reads:

If $H$ is a fixed group, show that $G\mapsto H \times G$ defines a functor,

$H \times - : \textbf{GRP}\rightarrow \textbf{GRP}$.

So is there a special meaning behind the notion '$H \times -$' ?

Thanks and cheers !