The definition of quotient group from mathworld.wolfram.com is:
For a group $G$ and a normal subgroup $N$ of $G$, the quotient group of $N$ in $G$, written $G/N$ and read "G modulo N", is the set of cosets of $N$ in $G$.
I don't understand the part "set of cosets of $N$ in $G$". Later it continues:
The elements of $G/N$ are written $Na$.
From this, I conclude that the expression "set of cosets of $N$ in $G$" means the set of cosets which have elements $Na, a \in G$. Is this correct?