Typically it refers to the centerline of the string travel in relation to the riser. Looking from the back of the bow it would be the path in relation to the perpendicular center of the riser that the string drives the arrow down. If a measurement is given for it the measurement is the distance out from the riser that the rest must be set so that the center of the arrow travels true to the center of the string.

It can also be used in regard to the horizontal center of the bow which refers to where the arrow is rin relation to the center of the string. You'll notice on most compounds that the grip is in the true center of the riser and the arrow is therefore above that point. There have been a couple attempts at bows with a true center shot arrow in this regard but the grip had to be below the center line and it made the bow feel top heavy when being drawn. Measurements and corrections dealing with this "center shot" usually deal with "tiller" or the difference in load between the top and bottom limb used to correct for the arrow not being in the centerline of the string. The actual position of this "center shot" is determined by the engineering of the bow and placement of the Berger hole (rest mount). There's not much that you can do to change it for a given bow.