If you're going to be able to write down very large numbers, you need a sensible system of notation. In the Roman system, the largest digit was "M", a thousand. So, to say ten thousand, you need to write MMMMMMMMMM. Cumbersome, and easy to make mistakes. In India, they developed a much better decimal system based on position, which is the one we use today. George Gheverghese Joseph is a math historian at the University of Manchester: "The place of a particular number determines what its value is. For instance, if you've got a number like "111", which is one hundred eleven as we understand it, the first "1" stands for a one unit. The next "1" stands for "tens". And, moving from right to left, the third of the terms, "1", means a hundred units. So, it's basically a hundred plus ten plus one." With a number system based on position, you can write big numbers easily. You only need seven digits to write all numbers up to a million. In the Roman system, you'd need to write a thousand M's in a line.
But a number system based on position requires a new mathematical concept, zero, for when there is nothing in that position. If we write "101", this is "1" in the "hundreds" position, zero in the "tens" position, and "1" in the "units" position. The Indians called zero "shunya", or "void". To give nothing a symbol, in other words, to say that nothing was something, was arguably the greatest conceptual leap in the history of mathematics. Neither the Greeks nor the Romans had a word or symbol for zero.
Audio source: http://www.bbc.co.uk/podcasts/series/discovery discovery_20131118-2100a.mp3 05:46-07:36