One can trade with the quartermaster and feel free to utilize his numerous crafting stations. Inspecting the tabletop map in the largest tent may potentially gain new map data as well. It is also possible to loot a few chests in the tents.
The soldiers will warn the Dragonborn to leave if they are a member of the Stormcloaks. If the warning is ignored and the Dragonborn remains at the camp, the soldiers will attack.