If you're disconnected from the internet while playing Diablo 3, your game instance freezes straight away and after a minute or so, you're booted back to the character selection screen. When you log back in, you restart from your last checkpoint - but keep any gold, experience and items you earned.
We tested this by disconnecting our wireless internet connection in Windows while playing. Here's a video of what happened:
Starting for a checkpoint early in the game, we gathered an item and some gold and killed a few monsters. Immediately after disconnection (the sound cuts out as we kill the connection in windows), monsters freeze and no objects in the game world can be interacted with. You can still run around for a minute, although in this randomly generated dungeon, the map can be seen to cut off in certain points where it should run on, with walkways abruptly ending in nothingness.
Eventually a prompt appears confirming the disconnection and taking you back to the character selection screen. Presumably this long delay is to allow for short connection dropouts.
On this occasion, attempting to resume the game after reconnecting to the internet prompted an error message and booted us back to the login screen. However, this didn't happen every time we tried this experiment - sometimes it was possible to rejoin straight away.
Just as if you'd logged out of the game normally, you start the game from your last checkpoint, and all monsters you've killed have returned. However, all character progress - experience, gold and items collected - is retained. This game information must be logged instantly with servers while playing.
Blizzard's requirement of a permanent internet connection to play Diablo 3 has been controversial with players who enjoy the solo adventuring aspects of the game. Previous games in the series allowed you to choose to play offline or on Battle.net servers, and also permitted LAN play.