Auburn is a reddish-brown color. If you ask a hairdresser to color your hair auburn, you'll be disappointed to end up with bright red curls.
Auburn almost always describes hair color — you might talk about your favorite childhood doll's long auburn hair, for example. The earliest meaning of auburn was "yellowish-white," not "reddish-brown," from the Medieval Latin alburnus, "off-white" or "whitish," from the Latin albus, or "white." In the 16th century it was influenced by the Middle English word brun, "brown," and the meaning changed.