What exactly does "Ghazwa-e-Hind" mean? How and when did such a term come into existence? Do Indian Muslims believe or support this theory?

Ghazwa-e-hind roughly translated as “Holy war against India”. This term comes from Sunan an-Nasa'i 3174 [1] , 3175 [2]  which is collection of hadith compiled by Imam Ahmad an-Nasa'i in later 8th century. This came decades after failure of Umayyad caliphate to break into Bharat. Successive attempts of Muhammad bin Qasim (712–715), Al Junayd (723–726), Al-Hakam (731–740) were ended in failure due to fierce resistance put by Bhartiya rulers.

Nagabhata of the Pratihara Dynasty defeated a major Arab expedition in Malwa. From the South, Vikramaditya II sent his general Avanijanashraya Pulakeshin, who defeated the Arabs in Gujarat. Later in 776 CE, a naval expedition by the Arabs was defeated by the Saindhava naval fleet under Agguka I.

Please note that Umayyad caliphate was only the second caliphate after prophet Muhammad, the legendary period in which these holy text/books and its interpretation is still being documented/written down. So the collapse of Umayyad caliphate left an un-fulfilled dream of capturing the coveted land of Bharat which was richest and most prosperous land of the era. As with other holy books which got documented decades later after the “revelation”, hadiths too are feared to be infested with personal political ambitions of the caliphate.

The referred hadith states that

The Messenger of Allah (ﷺ) promised that we would invade India. If I live to see that I will sacrifice myself and my wealth. If I am killed, I will be one of the best of the martyrs, and if I come back, I will be Abu Hurairah Al-Muharrar.

Even though Al-Nasa'i was credited with such a momentus hadith, he had limited knowledge about Umayyad caliphate, which later became cause of his own death. In 915 AD he visited Damascus and decided to deliver a lecture at Umayyad Mosque. But lack of indepth knowledge on the subject and indecent remark on Muawiya (founder of Umayyad Caliphate) riled up the crowd so much that Syrians crushed Imam Nisai's testicles and cut open his stomach resulting in his death.

So this hadith which literally means “saying” was recorded 200 years after originator (prophet muhhamed) death and was recorded by someone who has limited knoweldge about caliphate’s misadventure into Bharat, raising doubt about the whole claimed “promise”. But then this applies for most of the hadiths, which muslims follows religiously.

Footnotes

[1] Sayings and Teachings of Prophet Muhammad (صلى الله عليه و سلم)

[2] Sayings and Teachings of Prophet Muhammad (صلى الله عليه و سلم)