Andromeda, which is also known as Gene Rodenberry’s Andromeda, was an idea of Gene Rodenberry, the creator of Star Trek, although he had died by the time Andromeda was actually made. His wife, Majel Barrett-Roddenberry (who herself starred in the original Star Trek prior to their marriage and later in The Next Generation and Deep Space Nine, albeit as a different character) produced the show.
The main character is Dylan Hunt, a captain in the High Guard of the Systems Commonwealth, and the commander of the Andromeda Ascendant, which is a Glorious Heritage heavy cruiser, that ship class being some of the most powerful ships in the High Guard fleet. The ship itself is run by an AI known as Andromeda (played by Lexa Doig, who appears in Stargate SG-1 and Continuum as well).
Following an ambush, the Andromeda Ascendant is left trapped near the event horizon of a black hole and suffers from the effects of time dilation. Time essentially stops for Dylan – the remaining crew having abandoned ship prior to it straying too close to the black hole – but, when the Andromeda Ascendant is pulled free from the gravitational influence of the singularity by a salvage ship, the Eureka Maru, 300 years have passed after the fall of the Systems Commonwealth, the ambush he was involved in being the start of the fall.
The Systems Commonwealth was an inter-galactic polity described as spanning three galaxies (although more than three are mentioned during the series), with the three galaxies in question being the Milky Way, the Triangulum and the Andromeda, the last being the home of the founders of the Commonwealth. The polity seems to have spanned much of the Local Cluster of galaxies.
Dylan intends to rebuild the Systems Commonwealth with the Andromeda Ascendant which is, following the fall of the original Commonwealth, one of the most powerful ships still around, although its crew is greatly reduced from the thousands it had at the beginning to just a handful of people, consisting of people that Dylan recruited following his escape from the black hole. Along the way, Dylan and his new crew face many enemies, the greatest among them being that of the Magog and their god.
The series ran for five seasons before it ended, with the main plot thread that started in the first series resolved in the final episode. Some of the episodes were stand alone; many ran with the common purpose of rebuilding the Commonwealth and defeating those who want to keep it shattered.
One common item was that the series had invented quotes at the beginning of the episodes. These quotes often had some sort of connection with the episode in question.
At times, the show gets a little weird. This becomes more common after the original showrunner left at the end of season two and the fifth and final season is definitely odd.