"AO" = Adjustable Objective (turret). Scopes of generally higher power tend to be used at several different ranges and need to be accurate at every range at which it's used. Thus, the Adjustable Objective turret (the front turret on the scope).
With an A/O, you'll notice that there are "marks" on the objective turret body with range designations under those "marks". The unit of measurement is in
YARDS, so "50" equals 50 yards or "100" equals 100 yards and the "infinity sign" (looks like the figure "8" laying on its side) is for the longer ranges beyond the largest designated range (in yards) on the objective lense's turret.
By putting the adjustable turret on the range at which one is shooting, one can avoid "parallax" which is a distortion of the scope's crosshairs at the target's range which can and does cause poor accuracy if not eliminated by the use of a scope with an Adjustable Objective turret.
Most
non-A/O center-fire rifle hunting scopes are set to be parallax-free at 100 yards. Rimfire scopes are suppose to be adjusted to be parallax-free at 50 yards.
I hope this helps...
Strength & Honor...
Ron T.