An Event generally refers to any sort of special thing in The World or The World R:2 that differs from the usual state of affairs in the game. Events are usually created and run by CC Corp though some, such as the .hackers character contest was run without the knowledge of CC Corp.
Events generally include mini-games like a puzzle dungeon, events related to specific holidays like the Tanabata Festival, or one time monsters such as the One Sin. Most are usually only available for a limited time, though others like the Zeit Statue event can be held for an undetermined period.