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 over their waist, while women tie them over their breasts.
Towels are for the most part used in the same way as they are in real life. They're 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. However, such towels are often used as a form of censorship, even worn during bathing.
In anime, these towels tend to be either white, light pink or light blue, but can obviously come in any color.
Despite the use of towels for censorship, seeing a character in nothing but a towel is also often considered a form of fan service. In the more fan service-heavy scenes towels have a habit of slipping off quite easily, though usually being caught before too much is revealed.