Parker O. (P.O.) Ackley was a gunsmith and experiementer starting in the 1920's. I don't know when he died. AFAIK he did not actually manufacture rifles or barrels, but put many together and was considered one of the best. His specialty was the development of the Ackley Improved line of cartridges. The improvement consisted mainly of blowing out the case shoulder to a rather steep angle, which he claimed increased velocity. Others claimed that the angle simply allowed him to put more powder in the case and that resulted in more velocity, as well as high pressures.
If the barrel is simply marked with his name, he most likely just barreled the rifle. If there is a caliber and Ackley Improved, then the rifle is chambered for one of Ackley's "wildcat" cartridges and is a handloading proposition, assuming dies can be found.
In either case, the rifle should be a very nice custom rifle.
Jim