An Adjustable Objective lens on a scope is supposed to correct parallax errors at different ranges.
The wikipedia entry on parallax describes the visual effect pretty good even though it's applying it to stars and telescopes instead of riflescopes and targets. Same concept.
Basically...if you do not get a good consistent cheek weld to your rifle stock to keep your eye in the same place with every shot, the point of impact can change. This error is parallax and it will vary at different ranges. An AO is supposed to help correct the error.
I've had a few scope with them and never really thought that I had a benefit from the AO. More important is getting your scope mounted on your rifle in a position that allows you to get a consistent sight picture every time you mount the rifle.