How much energy a light gives out at each wavelength — the light's full recipe, of which its colour temperature is only a summary.
A function of wavelength, usually plotted from about 380 to 780 nm. Two lights with the same correlated colour temperature can have very different distributions and so render surfaces differently.
Kelvin alone does not describe a light. A 3000 K LED and a 3000 K halogen lamp look similar as light but can make the same fabric look different.
Low-pressure sodium street lamps emit almost all their light near 589 nm, which is why colours vanish under them.
It is the reason colour rendering, metamerism and 'this paint looks wrong under my lights' exist at all.