Conformal fuel tanks (CFTs) are additional fuel tanks fitted closely to the profile of an aircraft that extend either the range or "time on station" of the aircraft, with a reduced aerodynamic penalty compared to external drop tanks.
Conformal fuel tanks have the disadvantage that, unlike drop tanks, they cannot be discarded in flight, because they are plumbed into the aircraft and so can only be removed on the ground. As a result, they may impose a drag-penalty on the aircraft, even when the tanks are empty, without any benefit. They can also impose g-load limits and they add a slight, though negligible, weight gain to the aircraft, even when empty. While the weight gain and drag penalty are always present, g-load limitation is not always an absolute issue. The CFTs on the F-15E actually allow the same maneuverability without g-limitations.
Other advantages CFTs provide is that they can free up hardpoints that would normally be used to carry weapons or fuel tanks and that they do not significantly increase an aircraft's radar cross-section.