Embryological definition: The encysted form of the fertilized macrogamete, or zygote, in coccidian Sporozoea in which sporogonic multiplication occurs.

Uhh… English?
Basically, an organism that has developed an outer protective wall as a means to transfer between hosts and multiply.

Think of it as the diving suit that a scuba diver wears (thanks to wertperch for the analogy). What is a diving suit? A protective layer that insulates you from the water, allowing you to survive in it (kind of an oversimplification, but run with it). In the water without a diving suit, you have a very limited area in which you can survive for any length of time -- the surface. So, too, is an organism limited to a few places that it can survive, unless it is an oocyst and has the protective wall -- inside of its host, certainly, and perhaps in whatever transfer medium it uses, for a short while at least.

One major difference between an oocyst and a diving suit that's worth mentioning: while a diving suit will allow a diver to survive underwater for hours at a time, the protective wall of the oocyst allows the organism to survive without a host for years, as well as protecting it from many harmful substances, including the chemical disinfectants like the kind used at water treatment plants.

There you have it, kids. Embryology 101 or, “Everything you never wanted to know about oocysts”. Class dismissed.

Sources:
http://www.dictionarybarn.com/OOCYST.php
http://yahooligans.yahoo.com/reference/dictionary/entries/39/o0083900.html (power to the Y!)
http://www.corid.com/coccidia.html