Mission Alpha
A Mission Alpha is a mission dry-run. This year's Mission Alpha is mission Daedalus. It's destination was pluto.
Historical
These were typically run about 1 month before the actual mission, and lasted about 4-6 hours in duration. The purpose was to test out all equipment, and discover any problems or areas lacking proper planning. It also was an excellent opportunity to test the level of training for both Astronauts and Mission Control staff.
In the 2001-2002 year, a Mission Beta was run. The Mission Alpha occured while the Habitat was still under construction, and as such a second dry run was needed closer to the mission date.
Mini-Missions
Mini-missions were historically an EEP activity for older classes. In recent years, Space Sim has taken to calling the dry-runs 'Mini-Missions' instead of Mission Alpha.