Ummah (أمة) is an Arabic and Islamic word that means "community" or nation. It is correctly used to mean the nation of the believers (Ummah Al-Muhmini) in Islam, thus the whole muslim world. The phrase al-ummatun wahid in the Quran (the "One Community") refers to all of the muslim world unified.
The Constitution of Medina, negotiated by Muhammad and accepted by the Mala [Senate] of Medina, explicitly refers to Jewish and pagan citizens of Medina as members of the Ummah or nation .
Modern Islamists use the term "The Islamic / Muslim Ummah" to refer to all the people in the lands and countries where predominantly muslims reside, where the khilafah state once ruled. They include non-muslims minorities. When they talk of unifying the "Islamic Ummah" they would include these non-muslims, as citizens of the Islamic Ummah, living peacfully with their own respective religions, paying more tax (called Jizya) than muslims, being loyal citizens of the khilafah state. Thus shariah or traditional muslim law can be claimed to extend to non-muslims within the Islamist state, who are thus equally open to prosecution, just as muslims would be, for crimes of "apostasy" or "blasphemy". The interpretation of these crimes is up to muslim judges, within the ummah.