Tattoos from real henna are pale red/brown. They look like a birthmark. The dye in henna, lawsone, bonds with proteins, so it stick to tissue from living things: skin, hair, fingernails, even wood. It takes hours or overnight for the dye to bond with the skin. To answer your second question, chlorinated water or soaps may react with the lawsone so it doesn't darken as much, although it's still present in the skin.

Be warned, most "henna tattoos", especially dark ones or quick ones, are made using a chemical called para-phenlenediamine (PPD). PPD is used so the tattoo bonds quickly--making "henna tattoos" popular for tourists, fairs, and festivals. These dark "henna" tattoos with PPD can cause severe allergic reactions with life-threatening consequences. There are even reports of people being partially paralyzed by a "temporary" tattoo. It also can cause permanent allergies to things like synthetic hair dyes, which could then be life-threatening for the rest of your life. Even true henna is currently considered dangerous to apply to the skin, even though some people still sell it. To be safe, keep black dyes off your skin--and especially warn young children not to take temporary tattoos (except from those in Cracker Jack boxes, which use different, non-black dyes).

Henna body art is done using a dye, called 'lawsone', that is extracted from the leaves of the henna plant.Lawsone, like many other natural dyes, binds to the proteins on the surface of the skin, which is why it can be used to make 'tattoos.' But unlike real tattoos, in which ink is injected beneath the skin to make a permanent mark, lawsone remains on the surface. However, lawsone does form a chemical bond with the keratin molecules in skin, so the only way for the tattoo to fade is for the outer layer of skin cells to rub off. This happens pretty rapidly, but water can help the process along. Water may also dissolve some of the dye that has not yet bound to the skin cells.

Wikipedia has pretty good entries on henna and lawsone.