The Stormcloaks are part of the Civil War Quest Line. They are a group rallying around Ulfric Stormcloak, the High King of Skyrim, in an effort to make Skyrim independent from the Empire seated in Cyrodil. Amongst his men, known as the Stormcloaks after their admiration for Ulfric, he is known to be a charismatic and fearless leader who is so powerful that he "shout[ed] the previous High King to pieces".
The Stormcloaks quest line is similar in many ways to the Imperial quest line but with different locations and occasionally with the same battles but on opposite sides. An important note is that during the main quest line, there will be a quest called "Season Unending" which can effect the way that the civil war battles play out.
For more information about the faction, please visit its faction page.