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.
The PLEX is a nice way to get the Eve Online Subscription for those that can't use the in-game method or, for some reason, just want to use an alternative to what already is. It's available 30 days since it was activated ; the biggest advantage of it is that it can be traded, which, for some users, definitely makes easier the process of getting a more time-lasting access to online features of EVE.