It is an Ohio State Militia uniform button, showing the State Seal of Ohio. There are several versions of OH Seal buttons. Your version is listed in the book on American Uniform Buttons by Alphaeus H. Albert as button OH-6a. The Waterbury Button Co. backmark with three stars indicates your button dates from 1890 into the early 20th-Century -- but no later than 1941, when the company changed its name to Waterbury Companies (plural).
After-posting edit:
Okay, Mud Hut gets credit for the first correct answer, because he typed a shorter answer than me. ;-)