Armenians come from HISTORIC ARMENIA, which is a much larger piece of land than the current Republic of Armenia (but includes all of that country). Most of Historic Armenia is in the northeastern portion of Turkey, but there are parts of it in the Republic of Georgia, Azerbaijan, Iran, Iraq, and Syria as well. Additionally, the Armenians were also an urban minority in major Ottoman cities like Constantinople, Sivas, and the cities of the Cilicia region.
See this link for an image of Historic Armenia and see this link for a map of urban Armenian populations in the Ottoman Empire prior to the Armenian Genocide of 1915.