The Imperials are in Skyrim to stop the Stormcloak rebellion. According to Imperials, the Empire can't exist without Skyrim and the Nords while Skyrim can't exist without the Empire. Furthermore, many Imperials don't recognize Ulfric Stormcloak as the heir to the throne of Skyrim saying that he murdered a child to take the throne.
The Imperials share the Civil War quest line with the Stormcloaks. Many of the quests are very similar but there are a few differences, especially depending on some of the options you may make during Season Unending. To begin the quest, you'll have to make your way to solitude and talk to Legate Rikke.
For more information about the Imperial Faction, please see this page.