PLEX is 30 days of game time in the form of an in-game item.
You can purchase PLEX here or from other players using in-game ISK. Many players pay their subscription simply by playing the game and buying PLEX on the EVE market.
PLEX is actively traded between players and can be found in every major trade hub of EVE Online. It is only consumed when you activate it, affording you the freedom to use it when and where you need it most.