Terran
The terrans of the Koprulu Sector are descendants of the criminal and unwanted elements of Earth, launched into space to make room on their homeworld for those more deserving.
Crash-landed on scattered worlds, the terrans adapted, expanded, and even began to thrive. Re-developing the technology and industry required for spaceflight, the isolated terran worlds were reunited and, inevitably, went to war, for all the same reasons that humanity has waged wars over their long history.
Ultimately the Terran Confederacy became the dominant power in the Koprulu sector. Rebels and revolutionaries lurked at the fringes, remembering the atrocities of past conflicts, but most terrans lived in peace and relative prosperity.
And then the zerg came, and in their wake everything changed.
The terran military makes extensive use of criminals, rehabilitated by chemical, psychological, and cybernetic means. Augmented with exoskeletal suits of powered armor and the most potent stimulants modern pharmacology can devise, these marines form the backbone of every terran fighting force. The addition of powerful siege tanks, battlecruisers, and other war machines gives the terran forces unparalleled flexibility and mobility.
The terran leaders are former Confederate marshal Jim Raynor and Emperor Arcturus Mengsk of the newly formed Terran Dominion. Raynor is a survivor of Mar Sara's infestation and incineration. Betrayed by both the Confederacy (which he helped Mengsk destroy) and then by Mengsk's followers, the Sons of Korhal, Raynor now leads his ragtag band of survivors towards an uncertain future. Arcturus Mengsk seized the opportunity inherent in the chaos of spreading zerg infestation and destroyed the Confederacy. Naming himself emperor of the Terran Dominion, Mengsk now looks to consolidate his power by destroying all who would oppose him.
Preview: the Terrans
An article by game designer Corey Konieczka with more details (and photos too!) about the terran forces.