Ummah is an Arabic word that means "community" or "nation". However, it is not a geography based designation. The word specifically refers to the worldwide community of Islamic people. The word has its origins in the Quran, where it is used to refer to all Muslim peoples.
The concept of the ummah was a unifying force for people in the Arabic world, who before Islam tended to be separated by tribes and kinship. When Islam arose, ummah acted as a driver of togetherness, bringing disparate peoples together by their shared bond of religious faith.
Historically it seems that ummah was developed by Muhammad specifically to unite Muslims, first in Medina where his people were based, and then gradually expanding to cover the whole Islamic world. It is believed that originally ummah also extended to Jews, as Islam was a direct descendant of Jewish faith, but eventually it morphed into being solely Islamic.