The Imperial Legion used to be the strongest fighting force in Tamriel. But by the time that The Elder Scrolls V takes place, the Legion is just a shadow of its former self. Many view the Imperial Legion as corrupt and decaying, because of the disappearance of the Blades and the growth of the Thalamor as a military power.
The Imperial Legion is based in Solitude and can be joined by the Dragonborn. If he joins the Legion, he can not join the Stormcloaks anymore since these two factions are at war with each other. The Legion is part of the Civil War Quest Line.
The Imperial Legion has the support of the Battle-Born clan and holds Falkreath, Markarth, Morthal and Whiterun.
For more on the Civil War Quest Line, please see the walkthrough.