Think of it like a 'density score' for light; just as a score out of 100 is just a number without a unit, the refractive index compares how slow light is in a material relative to a vacuum.

The refractive index ($n$) is calculated by the ratio of two speeds: the speed of light in vacuum ($c$) and the phase velocity of light in the medium ($v$). Since both $c$ and $v$ have units of $m/s$, the ratio $\frac{m/s}{m/s}$ results in a pure number with no units.

Always remember that any physical quantity defined as a ratio of the same units (like strain, relative density, or refractive index) will always be unitless.