Step 1: Understand what is being asked.
We need the quantum number that tells us the shape of an orbital. Each of the four quantum numbers describes a different property of an electron, so let us go through them one by one.
Step 2: Recall the principal quantum number $n$.
The principal quantum number $n$ describes the main energy level or shell and is the main factor deciding the size and energy of the orbital. It does not describe shape.
Step 3: Recall the azimuthal quantum number $l$.
The azimuthal (or angular momentum) quantum number $l$ defines the subshell and decides the shape of the orbital. For example, $l=0$ gives a spherical $s$ orbital, $l=1$ gives a dumbbell shaped $p$ orbital, and $l=2$ gives a more complex $d$ orbital.
Step 4: Recall the magnetic quantum number $m_l$.
The magnetic quantum number $m_l$ describes the orientation of the orbital in space, that is, how the orbital is tilted along the axes, not its shape.
Step 5: Recall the spin quantum number $m_s$.
The spin quantum number $m_s$ describes the spin direction of the electron, either $+\tfrac{1}{2}$ or $-\tfrac{1}{2}$. It has nothing to do with shape.
Step 6: Pick the correct option.
Since only $l$ governs the shape of an orbital, the answer is the azimuthal quantum number.
\[ \boxed{\text{Azimuthal quantum number}} \]