Now Shelley gives a good example - the snowshoe hare which changes color annually: it is dark in summer and white in winter. It is pretty easy to remember - it's all the Mel-something molecules involved. So, here is a very simplified, but essentially correct description of how this happens:
Light is detected by the photo-pigment melanopsin in the retinal ganglion cells of the eye. The cells send a signal to the clock (in the suprachiasmatic nucleus, SCN).
SCN sends a signal to the pineal gland. During the night, when it is dark, the pineal gland responds to the SCN signal by synthetizing and releasing the hormone melatonin into the bloodstream. The duration of the melatonin release is an indicator of the length of the night: long night = winter, short night = summer.
Melatonin receptors are found in the SCN, in some other places in the brain, and in some other places in the body. In the snowshoe hare, one of the targets of melatonin is the hypothalamo-pituitary system that controls the deposition of the pigment melanin into the hair follicles.
Thus, in summer, melanin gets deposited into the hair follicles and the hair that grows out of them is dark. At the onset of winter, when the clock starts detecting the shortening of the day (i.e., lengthening of the night-time melatonin signal), melanin is supressed and the dark hair is replaced with white hair (and more of it) instead.