For every $x \in G$, there is some $y \in G$ such that $x=y^2$. (This is the same as saying that every element of G has a square root)
Now, I'm not sure but I've been trying to think of counter-examples and I thought of the group of integers under multiplication.
Because if $x=5$ there is no integer $y$ where $y^2=5$
Is this right?