Three factors of equal importance and nearly simultaneous in the archaeological/anthropological sense (that is they were developed over a few centuries in various parts of the world).

1) Agriculture 2) Domestication of a number of animals

Obviously the third factor being the ability of cutting and profiling stones (mostly silex and obsidian) into object and tools that could be useful. The name of the era (Neolithic) actually means “new stone” and is successive to the Palaeolithic era (old stone) when rocks were used as they were with no attempt to modify their shape.