Live is a software development term that is used to describe the current build that has been released into production. In layman's terms, it is the latest set of changes to the game, i.e., "The item was never released for live; it only existed in Beta." This is also contrasted with the builds released on the Public test realm.
In World of Warcraft EditThis section concerns content exclusive to World of Warcraft.
In World of Warcraft, live realms are the ones that players usually play on and should have persistent player character data and state (achievements, events, quests, etc.). The character data and state on the PTR can be reset at any time, but players can import a snapshot of a live character's data and state from live realms.
Pre-release realms (Alpha and Beta) and the Public test realm will not have persistence beyond their intended test periods.