The technology of the New Stone Age that had the most impact on daily life is agriculture.
The New Stone Age refers to a period of Pre-History usually called Neolithic, which in Latin means exactly New Stone. This is the last stage of the stone age and it is characterized by the use of polished stone, which differentiate it from the Old Stone Age, or Paleolithic, that saw the development of carved stone which was rougher. But the most important technology invented in this period that changed completely the form of life of people was agriculture. It started around 10 thousand years ago in Mesopotamia in the Middle East and, slowly, it expanded to other regions of the world.
Before this invention, the economy was based on the recollection of resources, like hunting and fishing, for this reason, tribes tended to move from one place to another in search for resources, in other words, they were nomads. But after humans started to grow crops, to control cultivation and to domesticate cattle, the economy shifted from recollection to production. This made small tribes to abandon their nomad way of life and to become sedentary.
Moreover, agriculture allowed these human groups to accumulate food for large periods of time, which permitted an unprecedented growth of the population, and it pushed people to observe and study the cycles of nature in order to control it. The increasing population required a new division of work, the establishment of new social structures and hierarchies, and the development of common systems of belief in order to create a social order that would allow cooperative work among a large number of people.
The invention of agriculture was a social and technological revolution that established the basis of what later would be large agrarian empires and civilizations.