WON, standing for "World Opponent Network", was an online gaming system developed by Sierra (the original publishers of Half-Life). Valve shut down the WON system in 2004 and reworked Half-Life to work with their own system run through Steam.
The term "WON Half-Life" refers to the pre-Steam version of Half-Life (in its entirety, not just the online aspect). This version is considered redundant these days, between the ease with which Steam Half-Life can be obtained and certain issues only present in WON Half-Life. Pirated versions of Half-Life tend to be the WON version, and using it is generally discouraged.