The Universal Transverse Mercator grid system (also known as UTM) was developed by the United States' Defense Mapping Agency (long before there was a NIMA appparently). In this grid, the world is divided into 60 zones, each 6 degrees of longitude wide. Zone 1 is from 180°W longitude to 174°W longitude, and Zone 60 is from 174°E longitude to 180°E longitude. In each zone, coordinates are measured north and east in meters. These values are the northing and easting of a coordinate.
The northing of the equator is 0 meters if measuring a point in the northern hemisphere, or 10,000,000 meters if measuring a point in the southern hemisphere. (This value is called the 'initial northing' and must be recorded for each point to determine whether it is north or south of the equator.)
A central meridian through each zone is assigned an easting value of 500,000 meters. Grid values to the west of the central meridian are less than 500,000; to the east, more than 500,000.
To be perfectly honest, in almost all cases this system is annoying to work with. The only saving grace is that because I'm using this system for a computer based GIS, I can convert meters to feet, and feet to inches, and inches to screen pixels based upon a scale. This system however has proven to be stupid. While it does permit the US military to have pin-point precision in locating places, it also means that a single miscommunicated number can mean disaster. One well known story supposedly involves a seal strike team phoning the pentagon and asking where they were, after getting the UTM zone for their aqueous landing wrong. (On the other hand, every system of measurement has the same problem when you communicate poorly. :)