It is called a "general service" button because it was issued to privates, corporals, and sargeants in every branch (Infantry, Artillery, Cavalry, etc) of the US Army. Because it was issued to every yankee enlisted-man, it is the most common civil war Military button. Civil war relic diggers & collectors have nicknamed it an "eagle button." That specific version of US Army "General Service" (enlisted-men's ranks) button was in use from 1854 to 1874.
Did you dig it in New Jersey? No civil war combat occurred in that state, so if you dug it there, it is from a training-camp. Newly drafted (or enlisted) soldiers received their uniforms and equipment and basic training at such camps, in their home state, before being sent off to the war as a regiment.