The Neolithic Revolution was the time, around 10,000 years ago, when agriculture was first developed. This happened, it is believed, as people domesticated wild plants that grew in the areas where they lived.
It should not seem so strange to us that this could have developed in many areas independently. After all, people in all areas of the world would have known about the plants around them. They would have known which ones had large seeds or oily nuts, for example. They would have sought these foods. Eventually, someone would have had the idea to plant the seeds in a given place. They might have noticed that plants were growing from places where seeds had been spilled near the people's camps. This would be something that could have happened in any place where there were seeds or nuts or other suitable plants.
People are very curious and very inventive. When presented with similar opportunities (plants), they will likely come up with similar ideas (agriculture). This is the most likely reason why the Neolithic Revolution was able to develop independently in various areas.