There are some misconceptions about this in India and Sri Lanka. Most people there think Jambudīpa means India. But some people argue that Jambudīpa is really Sri Lanka. Both are wrong per Tipitaka.
In the Paṭhamakosala Sutta (AN 10.29): “Yāvatā, bhikkhave, candimasūriyā pariharanti disā bhanti virocamānā, tāva sahassadhā loko. Tasmiṃ sahassadhā loke sahassaṃ candānaṃ sahassaṃ sūriyānaṃ sahassaṃ sinerupabbatarājānaṃ sahassaṃ jambudīpānaṃ sahassaṃ aparagoyānānaṃ sahassaṃ uttarakurūnaṃ sahassaṃ pubbavidehānaṃ ..”
Translated (from the link below): ““Bhikkhus, as far as sun and moon revolve and light up the quarters with their brightness, so far the thousandfold world system extends. In that thousandfold world system there are a thousand moons, a thousand suns, a thousand Sinerus king of mountains, a thousand Jambudīpas, a thousand Aparagoyānas, a thousand Uttarakurus, a thousand Pubbavidehas, and a thousand four great oceans; a thousand four great kings, a thousand heavens ruled by the four great kings, a thousand Tāvatiṃsa heavens..”
A fairly good English translations is at: Kosala (1)
This is an interesting sutta that provides a lot of information on Buddha’s world view 2600 years ago. Here are some key points:
- There are four “dīpās” inhabited by humans centered on the Earth (in bold in the above paragraph). Jambudīpa is just one and it includes all the countries, not only India and Sri Lanka.
- The other three “dīpās”, we cannot see. They exist around the Earth, but are invisible to us, just like deva and brahma realms are also invisible.
- The sutta describes 1,000 “world systems”. Each one is centered around a star (our star is the Sun). Each of those “world systems” has 31 realms associated with it; each has those four “dīpās”.
- However, a Buddha is born only in our world system (within the 1,000 world systems), i.e., only in our Jambudīpa.
- There are an uncountable number of such clusters of 1,000 world systems in the universe (according to Buddha Dhamma). Such clusters are well-separated, and there could be Buddhas born in each of those.
- No one but a Buddha can even travel to another “1,000 world system”. Brahmas and Devas from our “1,000 world system” can visit Earth. For example, Dhammacakkappavattana Sutta says Brahmas and Devas from our “1,000 world systems” were present to hear that first desana by the Buddha.
- Furthermore, according to modern science, the separation between two adjacent “world systems” or “star systems” is several light years. That means to get to the nearest “world system” it will take say at least five years travelling at the speed of light. Since only a fraction of that speed can attained by a spacecraft, it is unlikely that humans will be able to travel even to the closest star system anytime soon. Maybe never.
- Finally, we must note that modern science was not aware of the existence of even our Moon, let alone any other “star systems with planets”, until Galileo (in the early 1600’s). This is clear evidence of the capabilities of a Buddha, and why we can have faith in his Dhamma (of course, practice provides more evidence too).
- Of course, the Buddha found out all these things about the universe without any telescopes. That shows the power of mind, when it is purified to the fullest.
This is a brief summary.
P.S. So, the meaning of the word, Jambudīpa, as pointed out by Vilas in his first post, is correct. A Buddha is born only in Jambudīpa.