Extropy is the opposite of entropy; while the universe may be slowly dying as all energy and order degrades into heat and chaos, some parts of the universe are going in the opposite direction. Against all reason, earth is covered in increasingly complex, ordered, and even goal-directed substances. Okay, it's a losing battle. But so far it's been pretty cool.
Extropianism is essentially the position that we should embrace extropy, and plan for it to increase, helping it when we can. It is closely tied to transhumanism, so it tends to go along with high hopes of life extension, the singularity, and mind uploading, but it also includes more immediate concerns such as robotics and space exploration.
Currently, extropianism is not winning the memetic wars, with terms like transhumanism being much more common, or being dropped altogether in favor of more specific terms for the various subconcerns of futurism. In 2010 Breki Tomasson and Hank Pellissier attempted to rebrand the movement as extropism, but this does not seem to be catching on.