Dear student,
When a beam of light is incident on a concave mirror it converges at a point after reflection, that means, the rays of light in the beam meets at a point after reflection. Like, a beam of light parallel to the principal axis will meet at the focus of the mirror after reflection. This is why it is called a converging mirror.
When parallel light rays fall on the surface of convex mirror then after reflection those rays seem to meet (diverge) at a single point but actually they do not meet. So, it is called diverging mirror.
Regards.