The Plot

The short version
The game takes place after the arrival of the UNS Calypso in the Beta Caeli star system. You take the role as captain of the Calypso. The Calypso has been sent from Earth to colonize the system. The UNS Tantalus was sent to the same star system after you, but because it makes use of a better engine, arrives in Beta Caeli before you do. The Calypso, Tantalus, and similar ships were sent to colonize other star systems due to the threat of humanity's extinction on Earth as a result of an interstellar war. The story involves the Calypso's attempts to find out what happened to the Tantalus and its colonies which have gone missing, as well as other mysteries involving relics of previous non-human inhabitants of the system.

The long version
This is from Michael Andersson's FAQ document, which is a valuable resource.

You are the captain of an interstellar seedship, the Calypso, sent out to colonize the Beta Caeli star system. Why? Because the Alpha Centaurians are attacking Earth, you're humanity's last hope, yadda, yadda, yadda, and it makes the game possible. Your mission is a follow-up to a previous ship, sent to arrive at Beta Caeli 21 years before you, but which seems to have completely disappeared. You and your advisors are in charge of setting up and maintaining vibrant, growing, and productive colonies around the new star system. During the game, you'll need to find clues as to what happened to the Tantalus, find things that help you develop new technologies, and just generally deal with whatever unexpected things any old seedship captain might have to deal with.

Even longer version
This is from Tom Ruschak who wrote a review close to the game's release date.

What you got here is a combination Sim-City/Starflight type game. This comes as no shock, since it was done by Joe Ybarra, who wrote Starflight 1 & 2. If you played & enjoyed either of those game, buy this one now. OK, a basic synopsis: you're the 2nd colony ship entering an unexplored new system. The nasty aliens have destroyed Earth, so you need to get this right, or there'll be no more human race. Unfortunately, you arrive some time after the other colony ship, and when you get there, you don't see a 'Welcome' mat..

You need to establish colonies (which run with a very simple sort of Sim-city sim), try and find out what happened to the other colonists by exploring, and research new and interesting things to help you to do these two things. Along the way, [spoilers deleted] and generally wander around the planetary system. BTW, just watching the planets & satellites go around the sun in the observatory is fun, and you actually need to plan trips for closest approach, a nice touch. Anyway, I won it in about 50 hours of game play. I paid $48 or so, and I feel I got maybe $65 in fun from it, so it was a good deal for me.