FIG. 1 is a left front elevated isometric view of the aircraft seat headrest; FIG. 2 is a top plan view of the aircraft seat headrest; FIG. 3 is a right front elevated isometric view of the aircraft seat headrest; FIG. 4 is a front view of the aircraft seat headrest; FIG. 5 is a right side view of the aircraft seat headrest; FIG. 6 is a back view of the aircraft seat headrest; and, FIG. 7 is a left side view of the aircraft seat headrest.