Online Play is an extra feature (does not require to be used in the game) that allows players to participate in Event/Daily Dimensions, see other players adventuring in leaderboard in the same dimension that the player is in, updates and more. Also players can tweet their end results on Twitter to warn their friends or show off.
During an online event, Ghosts of slain players will appear in your world around at the location they died from. They are not aggressive to the player, but will attack monsters.
Talking with Ghosts will give the player bonus experience (+50% XP) and other beneficial effects may happen, such as receiving items, or having your HP healed.