Ummah in the Quran
It is used for non-Muslims as well. Here, the purpose of Ummah is a large group of people that have the same language or religion or have the same geographical land.
This word (Ummah) has come 65 times in the holy Qur’an (Singular and plural). Its meaning in the Qur'an is people (Surah Al-Baqarah(2):213) and likewise humans who have religious union(3:110, 2:143). Frequently, it has come in the narrations as Ummatl-Muhammad or Ummati or Ummam, and it means a school or group that follows a prophet. Ummam also is applied as prior kinfolk and nations that Allah has sent them a prophet.
Different dimensions of the concept of Ummah in the Islamic culture (in short):
1: Islamic Ummah, successor of the prior Ummam
2: Ummah as the heir of the earth
3: Ummah and Sunnah
4: Amrel-Ma'ruf wa Nahi Anel Monkar (أمر المعروف و النهی عن المنکر )
According to another definition, In accordance with Sura Al-Anbiya verses 92-94:
The Arabic word /ummah/, according to Mufradat by Raqib, means any group or nation that a common cause joins them to each other, such as being common in religion and creed, being in the same time or Age, and being in one definite place, whether this unity is optional or non-optional.
Some commentators have considered the phrase: ‘single Ummah’, mentioned here, as ‘a single religion’.
Some others have said that the objective meaning of ‘Ummah’, in this verse, is the whole mankind in all ages and times.