Plumbing garbage disposal
With the disposal off look at the bottom, some models have a socket that will accept an allen key and allow you to rotate the shredding disk manually to clear clogs. If not you can do it from the top with either a special purpose wrench or a couple of pieces of broomstick. 



Inside the disposal is a rotating plate, with two cutter mounted on opposite sides. You lower the wrench, or two stout (something that won't break) pieces of wood down through the throat, then rotate it so it contacts the cutters. That allows you to rotate the disk by hand until it's unstuck. Once it's turning freely you can remove the tool and run the disposal to finish it.

All of this is assuming you didn't get something that shouldn't be in a disposal stuck. If you filled it with horse hair or iron filings you'll need either a new disposal, a plumber, or both.