This is going to be a long post, because trying to articulate the boxing process via written word is going to require some in-depth explanation...get comfortable and grab a beer for this-it'll probably be a long read...
A scope works reliably on several principals, but two of the most critical are alignment of the lenses, and the stability of the reticle in relation to the windage and elevation knobs and their mechanical attributes. If the lenses get knocked out of place, it changes the refraction of the image and light onto them, and distorts the image that the shooter sees, thus throwing off the zero. If the mechanisms that influence the adjustment of windage and/or elevation get knocked out of whack, it will obviously immediately effect the zero of the weapon. These inherently fragile attributes create common issues when a rifle takes a substantial blow from falling over or being dropped, but equally as common are scope mounting hardware issues. Boxing a scope is a sure-fire way of determining if any damage has been dealt to the actual optic, so that you can rule out one or the other, either the scope or the mount.
Scope boxing is essentially a two-step process, and unfortunately, it's a pain in the ass. The first step is to check the scope for "mechanical accuracy". to do so, you need to take it out of the rings. Once you've done so, you need to set it to a "mechanical zero".
To set a scope to it's mechanical zero, you need to pick a knob-either windage or elevation. Lets say for the sake of this post that we choose elevation. You need to turn that knob all the way to it's maximum potential one direction or the other-up or down. You'll then need to turn it all the way to it's polar opposite, and count every click within it's range...let's say hypothetically that that number of clicks turns out to be 70. You need to divide that in half, and now turn the knob the other direction 35 clicks...You have now set this axis exactly half way through it's range. Now repeat this process for the other turret. By logic, you have now set the reticle to it's exact center within the optic's tube.
Now, you need to build yourself a very stable platform-such as a heavy table that doesn't wobble when pushed. Get yourself a shoe box, and cut a "v" shaped channel in the short side of the box for the scope to lay in-with it's turrets in the middle...only the scope's body (tube) needs to contact the box-never the "bells" where the objective/ocular lenses are housed. Set your shoebox with the scope cradled in it on the tabletop, and aim it at a clear backdrop that you can mark on-such as a piece of paper taped to a wall. This can technically be done at any range, but I have found that 25 meters or so works fine.
Adjust your focus settings on your scope so that you have a crisp image, and if you have a parallax adjustment, then set that to it's optimal setting for the range you are working with. Draw a dot on the paper you are aiming the scope at, and move the box so that the cross hairs intersect as close to the dot as possible.
Now, look through your scope and acquire a good sight picture of the reticle on the dot. As you do this, slowly and gently rotate the whole scope around in a circle, so that the windage and elevation turrets make one complete revolution around the body of the scope. While you are doing this, observe the reticle's position on the dot. Since the scope has been returned to mechanical zero, the cross hairs should remain centered on the dot, and the exact point where the vertical and horizontal stadia lines intersect should not "roll around" and come back to the dot after a full revolution. If the cross hairs do indeed roll, then there is a problem; Either you did not correctly achieve mechanical zero, or your mechanical zero point is not true to your windage and elevation knobs. Obviously, the first one is a result of human error, and the second is really not a big issue, so long as it's not extremely out of whack, and it's repeatable. (we'll get to checking the repeatability a little further down.) There is one other issue that you can discover by this method that can prove to be catastrophic, and that is if any of the lenses have been knocked loose or out of alignment. Checking for a loose lens is pretty simple...just pick the scope up out of the cradle, and give it a firm smack against the meaty part of your palm. Now set it back into the cradle, repeat the rotation process, and notice if there are any changes. If there are, then you can stop right there-your scope is screwed, and it's time to either consult a repairman, or replace it. If it still holds the same aim point, then you should check to see if any of your lenses have been knocked out of alignment. To do so you'll need a flashlight. Aim the flashlight's beam st the objective lens of the scope, but do so from an oblique angle of about 45 to 70 degrees to the surface of the lens, roughly five feet or so away from the scope. Now once again look through the scope, and rotate the scope in the cradle the same way as before. This time, you are looking for apparent differences in the way the light is transmitted through the scope, particularly on the outer edges of the field of view. This should be pretty obvious, as any lens within that tube that is out of alignment will shift it's relative position within the tube upon rotation, and effect the way the light transmits through it.
A lens knocked out of alignment isn't necessarily a show stopper, so long as it will no longer move again-which is almost impossible to ascertain, but the fact is that if it's not severely out of alignment to the point that it is drastically warping the image, and it will no longer move, then it can be worked with.
If your scope has survived all of these tests and you're satisfied with the results, then you can now check the windage and elevation adjustments for repeatability. Return the scope to the cradle in the box, and aim it once again at the paper. You don't need to worry about re-aligning the reticle with the dot, but you will need to recruit the assistance of a friend or family member, and equip that person with a marker of some sort.
Now, rotate your windage knob all the way to the right, and your elevation knob all the way down, so that the reticle is at it's maximum bottom-right ordinate. Have your assistant place a mark on the paper at the point where your cross hairs now intersect. (you'll just have to "talk them in" as to where you need the dot.) From this point, it is absolutely critical that you DO NOT MOVE THE SCOPE'S POSITION IN THE CRADLE. If you do, then you'll need to start all over again.
Once you have made the mark on the paper, rotate your adjustment knobs so that the reticle moves to the top right ordinate. Have your assistant again mark this position on the paper. Repeat this process again for the top-left, and bottom-left ordinates. At this point, you should have four dots on your paper, representing all four of the extremes of your scope's adjustment range, making up the four corner points of a square, or a box-which is where the term "boxing" comes from. Now that you have established these four points, repeat the process again, carefully adjusting your scope back through all four extremes of the scope's adjustment range without moving the actual scope. If the scope's turrets are functioning properly, the reticle should end up exactly on the dots corresponding to each extreme the second time around. If they do not return to the dots, then there is most likely damage to the mechanics of the turrets, and the scope will not repeat zero.
Once this test is completed, it is a good idea to return the scope to it's mechanical zero once again, using the method described earlier, and rotate it once more in the cradle, just to make sure that it will still rotate on it's correct axis. If all of these test produce the desired result, then it is safe to assume that the scope is functioning properly, and the error is most likely within the mounting hardware. If the scope fails any or all of these tests, then it is probably due to damage to the scope itself, and it will either need to be repaired or replaced.
Man, I hope that made sense...I tried to scratch out some drawings on paintbrush, but I get defeated pretty regularly when I try to attach pictures to these posts.
