actually.. it's a bit more than that
lol Spoilers below
Starcraft
Human Campaign
Human faction was in control (Confederacy) and a strange new alien race was bombarding their planets on the fringe worlds. You, a commander in the confederacy, go to one outer planet, Mara Sara, to bring martial law to the planet. Well, you find another race there, the Zerg. You find out the Zerg have infested some terran facilities. Destroy them, you and the martial there (Jim Raynor and his group) are then under arrest by the Confederacy (General Duke) for destroying a confederacy compound. You are rescued by Arturus Mengsk who's part of another Terran faction. Anyways, you join Arturus to learn that the Zerg are being used by the Confederacy so they can have more power and that these other aliens (the protoss) are bombarding the planets to try and eradicate the Zerg. You destroy the Confederacy by turning the Zerg against them and their main planet. Then you take over, but by doing so have to keep the protoss from interfering with Zerg destroying the confederacy, and so Kerrigan (a subordinate of Mengsk's) is lost. You and Jim Raynor leave and the last fight is you having to fight off Mengsk' forces and destroy a super canon thing of his.
Zerg Campaign
You're a Cerebrate that has awoken, the Overmind has ordered you to watch over a crysalis of his. So first three or so missions you're defending it and then watching it until it awakens when it turns out to be Kerrigan.. but an infested one

so super Kerrigan! Then, you and Kerrigan destroy Protoss that are trying to destroy you, being led by Tassadar. You find out a Cerebrate has been killed, normally a Cerebrate's death is meaningless cause the Overmind can regenerate them but the protoss have a weapon that can neutralize the Overmind's powers. Anyways, you learn that these special Protoss, the Dark Templar, are on Char (the planet you're on with the Zerg) and so you have to hold them with the overlords and stop protoss and whatnot. Basically, in the end of that bit, the Zerg find out the Protoss homeworld cause of the Dark Templar, Zeratul, that killed the Cerebrate, when he did that, touched minds with the Overmind for a bit and so the Overmind can finally complete his desires. Anyways, Kerrigan stays back on Char with some Zerg and is hunting down Tassadar. You (a Cerebrate) and the Overmind and most of the Zerg forces go to the hidden homeworld of Aiur. You go there and basically prepare the way for invasion, destroying a temple of the Xel'Naga (ancient race that, at this point, you don't know too much about) so the Overmind can plant himself there.
Protoss Campaign
You're a new executor of the Conclave. They ordered you to secure some city of their world. After that, Tassadar comes back, thought to have failed, explains that Cerebrates killed will seriously aid, so the Protoss attack a Cerebrate but it regenerates. Then he tells them that it failed cause they need the aid of the Dark Templars. Because the Dark Templars are exiled from Aiur, they aren't seen highly by the Conclave. Well, eventually you and Tassadar go to find Zeratul. You do, return to Aiur, go to kill the Zerg but the conclave demands to have Tassadar to pay for his crime (he was supposed to eradicate the planets RIGHT away, he was trying to spare human casualties and so that pissed the conclave off cause it allowed Zerg to escape and such). Tassadar eventually surrenders cause he can't stand to see his people fight each other.. so then you, Jim Raynor, and Fenix (another protoss hero

) go to save Tassadar from execution, you do so, Conclave come to try and interfere, Zeratul comes with dark templar and so you guys escape. Then you go and attack two Cerebrates, weakening the Overmind's defenses, you then attack the Overmind head on.. and BOOM!! Tassadar sacrifices himself to destroy the Overmind.
Brood War
Protoss Campaign:
You're the executor and trying to help get your people off Aiur, it's far too ruined now and the Zerg, despite the Overmind being destroyed, are still far too deadly. So you leave Aiur for Shakuras, ancient homeworld of the Dark Templar (Protoss live for a LONG time). So there you reestablish yourselves, you learn Zerg have come through the warp gates too, you have to fight for securing the planet, Kerrigan comes, asks for your help, explaining that the Cerebrates are trying to make a new Overmind, she's free of his mind control so she's good again. Well, turns out she wasn't so good. Anyways, it ends with the Protoss using a Xel'Naga temple to destroy all Zerg on the planet (after you got two crystals for it).
Human Campaign:
UED, United Earth Directorate or something like that.. I forget, well they have formed their force and come full force to take control of their outer fringes (the confederacy places, which is now called The Dominion under Emperor Mengsk). They also have come to take over control of the Overmind. Anyways, essentially they do so. Become a HUGE power house because they control most of the Zerg (other than what Kerrigan has control over), and their overwhelming forces.
Zerg Campaign:
Kerrigan goes to, now defeated, Emperor Mengsk, Jim Raynor, and Fenix for help. Saying that the UED is a far worse enemy than anyone else. Anyways, they meet up with a UED traitor, Duran, who helps them overthrow the UED. They kill the Overmind (breaking the Zerg control from the UED), and then attack the UED. After, Kerrigan breaks their treaty and betrays them, killing Fenix and General Duke and weakening Mengsk's and such force's. The last battle is Kerrigan's little force (as most the Zerg are still slowly coming under control and are on the planet below) having to defend and destroy Emperor Mengsk', the remaining UED, and the Protoss' fleet under control of Aldaris. When you (she) wins, Kerrigan takes over as the main power in the area.
Secret Mission: There's a secret mission that does come up where you are the protoss commander Zeratul and you land on a planet.. finding weird experiments going on. combining Zerg and Protoss to create.. odd things. You find out Duran is doing this, on his own, and he claims he's still lying in wait for his Masters to return. Masters that are not Zerg, Protoss, or Terran, from what I've gathered
And that's kinda Starcraft's story in a nutshell. There's really a lot more to it but I am too lazy to write more.