Shooting an arrow through paper allows you to see what it is doing at a specific point in it's flight. You can see if it's coming off the rest straight or not.

For example, if it's coming off with the nock end higher than it should be you will get a vertical tear in the paper. If you look closely, you will be able to see the tears of the fletching at the top of the tear. But only if the paper is withing a few feet of the bow. Further out the fletching will overcorrect and the fletching tears will be on the bottom end of the tear. In this case you would lower your nocking point on your string a little.

For more on this, download the Easton Tuning Guide.

Paper tuning can be a very effective tool for getting good arrow flight. However, it is not the only tool and it has some limitations. The biggest limitation seems to be that the archer has to have good form, especially the bow hand. It's very easy to torque the riser a little and get false readings on the paper. I've read many posts where someone discounts the effectiveness of paper tuning. I think that most of these archers simply don't have good enough form to be able to get consistent and meaningful data from the paper.

Most archers use paper tuning as a first basic step in tuning their bows. Then they move on to other methods, such as walk back, bare shaft and group tuning.

Hope this helps,
Allen