A warp profile is a set of sensor readings describing the various attributes of a vessel's warp propulsion system.
In 2375, Kathryn Janeway, captain of the USS Voyager, ordered the energy output of a shuttlecraft's warp profile increased, in an attempt to make the shuttle a more appealing target to a Borg sphere. The plan worked, and the Borg detected the shuttle's warp signature, and proceeded to assimilate it. This provided a distraction which Janeway and a boarding party used to beam aboard the sphere and steal a transwarp coil. (VOY: "Dark Frontier")