I often see this technique suggested as a way to speed ripening. Why does it?
Also, is there any data available on how fast it ripens comparatively?
The ripening itself is caused by ethylene gas released by the food, which is trapped by any kind of bag.
As far as I know, there's nothing inherently special about a brown paper bag, other than the fact that it's porous and thus still allows some air to get in and out. Plastic ziplock bags have no ventilation, so they don't work nearly as well.
Placing fruit in a bag will help hasten the ripening for only a few fruits. Most fruits will not ripen (ever) once they have been picked. The only fruits that ripen once they're picked are bananas, avocados, pears, mango, and kiwifruit. Ripeness in fruits is based on sugar content, not color, thus most tomatoes in grocery stores have no flavor because they were picked green and exposed to ethylene gas to induce color change. Tomatoes are what are known as a "climacteric fruit" which means they'll change appearance based on climactic conditions but they don't ripen. Yes, they continue to soften but that's simply the process of cell deterioration know as decomposition.
Some fruits such as peaches, plums, etc. will seem to develop more sweetness as they sit on the counter but that's because they're also losing moisture and the residual sugars are concentrating in the cell walls.
Placing fruit in a paper bag helps to concentrate the levels of ethylene gas which is what helps induce the ripening of the above mentioned fruits (bananas/avocados, etc.). In fact, avocados and pears must be picked in order to ripen. Pears that are left on the tree will simply rot. As mentioned previously... brown paper bags used to be something everyone had around their house so it was a commmon item before the switch to plastic bags.
Have you ever noticed some people like red bell peppers and not green ones? The reason is due to ripeness.
The secret is that the fruit produces ethylene (a hormone found in plants), and ethylene promotes ripening. By placing fruit in a paper bag the ethylene collects (rather than dispersing in the room), increasing the concentration around the fruit and speeding ripening. About.com has an interesting article on ethylene and fruit ripening called Fruit Ripening and Ethylene Experiment.
Some types of fruit ripen with increased ethylene production and a rise in cellular respiration (the ripening fruit draws in oxygen and gives off ethylene). This happens in "climacteric fruit": Apples, bananas, melons, apricots, and tomatoes, among others (citrus, grapes, and strawberries are non-climacteric--you can do a search for "climacteric fruit" to see which are and which aren't).
The ethylene produced during respiration enhances the ripening process so when we put climacteric fruit in a paper (or plastic) bag, "none" of the ethylene can escape, thereby exposing the fruit to more and more ethylene as it continues to ripen. Paper bags only restrict oxygen flowing in/out of the bag while plastic prevents essentially all oxygen flow. Since climacteric fruit need oxygen for respiration, closed plastic bags will limit the amount of respiration to that allowed by the oxygen trapped in the closed plastic bag. Opening a plastic bag will allow some oxygen in (while letting some ethylene out)...in that case fruit will ripen faster with an open plastic bag than fruit just sitting on the counter but will ripen slower than in a paper bag because the paper keeps more ethylene in while still allowing oxygen in.
The short answer is that paper bags keep the ethylene trapped in the bag which enhances the ripening process while at the same time permitting some oxygen to enter the bag, allowing the fruit cells to respirate and produce more ethylene. Assuming brown paper bags are the same as other paper bags, then this should be true for brown paper bags as well.
I've never heard this, but ripening is usually sped up by various airborne chemicals functioning as plant hormones. This is why one bad apple will cause others to go bad - it is signalling them. So I suspect it is either a matter of enclosing the airborne chemicals, or that paper bags release some such chemical.