Coherent waves are all of the same frequency (monochromatic) and all the waves are in phase (that is, all the waves are "up" at the same point). Laser light is coherent.
A red light can be monochromatic but still be incoherent because the waves are in random phase. Actually, an incoherent wave would have some dispersion in its Fourier transform, although it might be quite narrow, but it can't be too narrow, or it would be coherent for all intents and purposes. White light is incoherent both because the phase of the waves are random and because white light is made of many different frequencies simultaneously.
