Classic is a title given to game modes released before Indev, namely Survival Mode Test and Creative mode (0.30).
The Creative mode doesn't support blocks made during or after Indev, items in general or any features like dynamic lighting introduced in Indev and later.
Classic mode doesn't support crafting, smelting, items, inventory, or movable stacks. There are no features that were made during or after Indev.
Classic is build-based and can be played in multiplayer; many different game modes are played, see "Game Modes" for more information.