As the Wikipedia entry explains, navy showers involve turning on the water, getting wet, turning off the water, lathering up, turning the water back on, rinsing off, and finally turning the water back off.
It means that while you’re standing there fussing with shampoo bottles and getting all sudsy, there isn’t any excess water going down the drain. By the time you’ve finished, the H2O should’ve only been running for about two minutes.
This idea originated on naval ships, where, ironically, supplies of fresh water were often scarce — now, many modern hippies have taken it up for both environmental and economic reasons. Whereas a 10-minute shower uses as much as 230 litres of water, a properly done navy shower usually only requires just over 10 litres, which means that over the course of a year, a single person can save up to 56,000 litres of this precious resource.