K is inverse of wavelength. It tells u the number of waves per unit length. Something like frequency tells u number of waves per unit time, but instead of time, it tells how many loops( wavelengths) are there in a given length.
In vector form, k becomes wave vector. Its magnitude shows wavenumber, but in vector form, it has a direction too, the direction in which wave is propagating. Its useful in higher dimensional waves. For 1 dimension, wave travels in the x direction only. But if its a 2d or 3d wave, then k gives the direction of wave.