Most electric guitars have metal bridges and saddles. These bridges are machined to factory specifications. Most likely you will never need to file down a metal saddle to adjust the bridge. If you ever did, you should probably buy a machinists file. Don't use one of your nice, sharp saddle files. The metal will probably ruin it. Acoustic guitars, on the other hand, have bone, plastic, or man made material saddles. These saddles often need to be shaped or filed down. This is what a saddle file is made for.
Since the saddle on an acoustic guitar is one of the only things controlling the action and playability of the guitar, it is important to properly set up the guitar saddle. A guitar saddle file is a sharp, usually thin, file. It is often times used to file the guitar nut and saddle. Check the action at the 12th fret on the guitar after you have straightened the neck and checked the action at the nut. If it is high, you may need to lower or shape the guitar saddle. Files are generally used to shape the saddleŚnot lower it. Since saddle usually only have to be lower a 64th or 32nd of an inch, sandpaper is better used to lower the saddle.
If your strings are breaking at the bridge, it generally means the saddle is too sharp. It should be reshaped. Take the saddle out of the bridge and place it in the saddle or nut vise. Now you can use the saddle file to take the sharp edge off of the saddle. Make sure not to take too much off the saddle, as that can cause other problems. That's all there is too it!
Saddle files can be used for many different things. After all, it is just a file. The main reason I like to have them is because they are sharp and meant for filing down common materials that nuts and saddles are made out of. You can use it to shape and file guitar nuts. I'd recommend getting at least one saddle/ nut file to keep in your guitar repair bench. If you would like more information about how to adjust your guitar action at the bridge, please see my how to adjust guitar action at the bridge article.