“Myo” means muscle. “Fascia” is the connective tissue that contains our muscles. The simplest analogy (really an over-simplification) is a sausage: muscle is the meat and fascia is the sausage casing (in fact, fascia pervades our entire body, connecting and running through organs and other tissues as well as muscles).
Myofascial release is a form of massage that is designed to get muscle fascia to move more freely. It is deep, slow work that helps to lengthen shortened tissues and separate tissues that shouldn’t be adhered to each other (another over-simplified analogy can apply here: picture two layers of Saran Wrap that have stuck to one another – now picture slowly and deliberately moving them against one another until they become unstuck).
Like all of the techniques I employ, I rarely do a full-on myofascial release session. Instead I incorporate it into the orthopedic massage protocols that I use.
Wikipedia offers a detailed look at the various aspects of myofascial release.