Conformal fuel tanks (CFTs) are additional fuel tanks fitted closely to the profile of an aircraft that extend the endurance of the aircraft.
CFTs have a reduced aerodynamic penalty compared to external drop tanks, and do not significantly increase an aircraft's radar cross-section.
Another advantage CFTs provide is that they do not occupy ordnance hardpoints like drop tanks, allowing the aircraft to carry its full payload.
As a result, they will impose a slight drag-penalty and minor weight gain on the aircraft even when the tanks are empty, without any benefit.
They can also impose slight g-load limits, although not always an absolute issue: the CFTs on the F-15E actually allow the same maneuverability without g-limitations.