From the Super Mario Wiki
Dream Events are extreme events in Mario & Sonic at the Olympic Games. They contain fictional or abstract features (items, special abilities, etc.) and must be unlocked.
Dream Events also make a reappearance in the sequel, Mario & Sonic at the Olympic Winter Games. They, as the ones before, contain fictional and abstract features as the ones before. They also need to be unlocked in order to play them. Unlike the Dream Events from the past game, these Dream Events take place in Mario and Sonic locations.
Dream Events re-appear in the Wii version Mario & Sonic at the London 2012 Olympic Games, which, unlike the previous games, are already unlocked. Dream Events do not appear in the 3DS version of the game.
Wii version events
DS version events
Wii U version events