The Greeks lacked a symbol and concept for zero. They wrestled with the philosophical implications of how nothing could be something.
The Babylonians developed an excellent sexagesimal number system (base 60) but they lacked the concept of zero. Over time, the Babylonians would develop a system of using a space as a placeholder between digits that functioned similarly to the modern zero. However, this space was not zero; the concept of representing nothing was foreign to them. Without the idea of zero, there was no way to distinguish certain Babylonian numbers, just like how today we wouldn't be able to distinguish the numbers 13, 103, 130 10003 without the use of zero.
The development of zero as an actual number (not just an empty space) is credited to 7th century Indian mathematics. Around the same time, the concept was being used by the Mayan civilization. However, it was the Indian concept of zero that spread to Arabia, Europe and China.
Indian mathematics treated zero like any other number, using it in calculations (even in division). It was the Indian mathematician, Bragmagupta, who first laid out a set of rules governing the use of zero. These rules included things like a number subtracted from itself is zero and a number times zero is zero.
The importance of zero can be summed up by Pierre-Simon Laplace, who said:
"The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated ... The importance of this invention is more readily appreciated when one considers that it was beyod the two greatest men of antiquity, Archimedes and Apollonius."