Infdev is a mode still under development, available only to those who have bought the game. Its main feature is generating maps of incredible size (8 times larger than the surface of the Earth, according to Notch). Currently, it generates strange landforms, including floating islands and strange looking cliffs that do not form normally in InDev. If you die, you can respawn at your starting point, but you drop all the items you were carrying (you can pick them up again if you can reach your body before the items expire).
Mobs and more realistic trees have been added on April 15th, 2010. Few more key features from Indev haven't yet been added, although Notch intends to re-add everything in upcoming updates.
Sometime in the future, Indev will become Infdev, but all original Indev maps will be able to be loaded into the updated version, says Notch[citation needed].