First, Danette, welcome to TreasureNet's "What-Is-It" forum, the best place on the internet for getting unidentified objects CORRECTLY identified.
The circular brass disc, showing a spread-winged eagle holding an olive branch and arrows in its talons, is a US Army model-1826 shoulder-belt plate (commonly known as an "eagle breastplate). That model was still in use in the civil war. The early version (1826-1831) had iron wire hooks or loops soldered directly onto the back of the brass disc. The later version (1832-through-1863), which is commonly found at civil war sites in the South, had its belt-attachment hooks or loops submerged in thick layer of solder on the brass disc's back. (Relic-diggers call that version a "lead-filled" back, but the filler-metal is actually solder, not lead.)
The most common variety, issued for use by Privates and Corporals, had two attachment-loops on the back. A much rare variety was made for Sergeants/Non-Commissioned-Officers, ranking below Commissioned Officers (Lieutenant and higher)... it had three hooks on the back. Please post some well-focused closeup photos of the back of yours, so we can give your a more-specific ID and time-period for it.