Great story, great gameplay, perfectly balanced and perfect difficulty curve. Starcraft is truly all it's made up to be.
There are three races. They are:
The Protoss, who are a group of highly developed and intelligent species. They also have psionic powers which they use in their weaponry. They are typically quality rather than quantity. All their units are extremely expensive, but they are also extremely powerful. They also are the only race which has shields. They do not heal at all, nor can they repair, but they have a structure called the shield battery which regenerates their shields.
The Zerg are like the creatures in the movie movie series "Alien". They are vicious, predatory and have a hive mind called the Overmind. They are quantity over quality, and will overrun a map given the chance. Their units are weak, but also cheap and quickly made. They're entirely biological, including their structures and facilities and all their units and buildings heal slowly over time when hurt.
The Terran. These are the humans, us. The terrans are also developed, if not as highly as the protoss, and are more versatile.
They are somewhat in-between the power of the protoss and the numbers of the zerg. They have the largest variety of units, ranging from the firebat, which has a flamethrower for close combat, to the siege tank, which has the largest range in the entire game. They also have some unique abilities like a ComSat station which explores the map using energy, and nuclear warheads later on in the tech tree. They can repair mechanical units with their basic builder unit and can heal biological units in the broodwar expansion. Some of their buildings can also fly and move around.
In the single player campaign, you get to play as all three races, to give you the feel of all three, as they are all unique.
Player vs Player is lots of fun, and most people generally realise they have a favourite among the three races so pick the one that suits you, and have fun.