A towel usually worn after bathing or showering to cover up. Sometimes used as censorship even during bathing.
A towel worn to preserve one's modesty, sometimes even when no-one else is around. Men typically tie them around their waist, while women tie them around their chest.
In anime and manga, as in real life, towels are generally worn after getting out of a bath, shower, hot spring, swimming pool etc. and before getting dressed. Understandably this is to get dry, stay warm and preserve modesty. This provides an easy form of censorship, and sometimes they're even worn during bathing, though this would seem to defeat the actual purpose of a towel.
In anime, these towels tend to either be white or appear in a variety of soft pastel colors including pink, blue, green and yellow.
Despite the use of towels for censorship, seeing a character wearing only a towel is also often considered a form of fan service. In the more fan service-heavy scenes characters in towels often fall victim to the dreaded wardrobe malfunction, though they usually catch the towel before too much is revealed. Unfortunately some characters don't notice their towel has fallen until it's pointed out to them.