Asia Minor is the area of the Asian continent encompassed by Turkey.

map via: http://www.lib.utexas.edu/maps/historical/shepherd/asia_minor_p20.jpg

It is basically the crossroads of Asia, Africa and Europe.  It was multi-ethnic for thousands of years.  Over time, Muslims from all over Asia settled in the area.  The area that the Christian Armenians inhabited is almost right in the middle of Asia Minor. They would face expulsion when ultra-nationalist Turks came to power. The conflict was that Armenians were Christian in a country which pressed for one religion (Islam). In a wave of Islamic fundamentalism, the Christian Armenians were considered infidels.