index of refraction
Light is famously the fastest thing there is, but only in empty space. Push it into water, glass, or diamond and it slows down, a lot. The index of refraction is a single number that tells you how much a given material slows light down, and therefore how strongly that material bends and steers light. It answers the practical question: is this stuff optically dense or thin, and how sharply will it bend a ray?
The definition is a ratio of speeds. If c is the speed of light in vacuum (about 3.0 x 10^8 m/s) and v is its speed in the material, then the index of refraction is n = c / v. Because nothing carries light faster than vacuum, n is always 1 or greater. Vacuum has n = 1 exactly, air is just a hair above at about 1.0003, water is about 1.33, ordinary glass is around 1.5, and diamond is a hefty 2.42, which is why it slows and bends light so dramatically that it sparkles. A larger n means slower light and stronger bending. The index also fixes the wavelength inside the material, lambda_medium = lambda_vacuum / n, while the frequency stays put.
You meet the index of refraction every time you specify a lens, design an optical fibre, or read Snell's law, n1 sin(theta1) = n2 sin(theta2), where the two indices decide how much a ray bends at a boundary. An honest subtlety: n is not quite one fixed number for a real material, it depends slightly on the light's colour (wavelength). That small variation is exactly what spreads white light into a rainbow, and it is called dispersion.
In water, n = 1.33, so light travels at v = c/n = (3.0 x 10^8)/1.33 = about 2.26 x 10^8 m/s, roughly a quarter slower than in vacuum. In diamond, n = 2.42, light crawls at only about 1.24 x 10^8 m/s.
n = c / v: a bigger index means slower light and stronger bending.
n is never less than 1 for ordinary light, because light cannot travel faster than c in a material. A high index means light is slower there, which is the opposite of what many beginners first guess.