Fort Dawnguard is the home of the Order by the same name. The Dawnguard are Vampire hunters and many of them are former Vigilants of Stendarr, an Order of Daedra Hunters. You will find many of the Order here including Isrun, their leader. New recruits are encouraged to visit to be evaluated and those that are allowed to join can find many places inside the fort or in the nearby lands to practics theirs skills.
Of particular note, the Fort of Dawnguard does not exist in the overworld of Skyrim and is part of a separate area near Riften. After talking to one of the guards in Riften, you'll be directed to the fort. You will be given a quest marker but the quest marker on your Compass and on your Map seem to disagree (unknown cause). You want to follow the marker on your compass to a cave. Going inside the cave will take you to an area just outside the fort.