I am reading p.22 of Dan Bump's Automorphihic forms and representations. A cusp of the congruence group acting on the upper half plane is defined to be an orbit of the action of the congruence subgroup on $\mathbb{Q} \mathbb{P}^1$. It also says that intuitively, the cusps are the places where a fundamental domain of the congruence subgroup touching the boundary of the upper half plane.
Question: Why does the definition mean what the intuition says?
Thanks!