I'll let Wikipedia supply the full definition for greywater:

Greywater, sometimes spelled graywater, grey water or gray water and also known as sullage, is non-industrial wastewater generated from domestic processes such as washing dishes, laundry and bathing. Greywater comprises 50-80% of residential wastewater. Greywater is distinct from blackwater in the amount and composition of its chemical and biological contaminants (from feces or toxic chemicals). Greywater gets its name from its cloudy appearance and from its status as being neither fresh (white water from groundwater or potable water), nor heavily polluted (blackwater). According to this definition wastewater containing significant food residues or high concentrations of toxic chemicals from household cleaners etc. may be considered "dark grey" or blackwater.

In recent years concerns over dwindling reserves of groundwater and overloaded or costly sewage treatment plants has generated much interest in the reuse or recycling of greywater, both domestically and for use in commercial irrigation. However, concerns over potential health and environmental risks means that many jurisdictions demand such intensive treatment systems for legal reuse of greywater that the commercial cost is higher than for fresh water. Despite these obstacles, greywater is often reused for irrigation, illegally or not, in older rural construction, simple construction old and new, often consisting of nothing more than a "drain out back" (pipe pointed down the nearest hill). In droughtzones or areas hit by hose pipe bans, typically by manual bucketting. In the third world, reuse of greywater is often unregulated and is common. At present, the recycling of greywater is poorly understood compared with elimination.

For more information and technical aspects of greywater systems, consult Greywater.com. You will find graphical descriptions and photographs of greywater systems that make it easy to visualize how they work and methods of implementation. Be sure to browse the "Contents" links for more in-depth studies and a planning page for those who might be interested in implementing their own greywater system.

Caveat emptor: although greywater systems seem like a natural fit for Southern California's water crisis, getting permission to install one may not go as smoothly as one might imagine. The Los Angeles Times recently ran an article that describes the bureaucratic nightmare that installing a greywater irrigation system can become.