They build irrigation systems to get water to their crops.
Do to the surplus amount of food, not every member of the community had to grow crops. this led to specialized workers.
Complex institutions made people recognized a need for a writing system to keep records.
Since everyone had a different job, they needed different items. To get those items they would trade with other members of their community.
I'll give you this wheat for your pot.
Communities would also trade with neighboring settlements if they didn't have a needed good.
Having specialized workers also created social inequality because some jobs were considered to be more important than others. For example the king and priest would be the highest members while farmers the lowest. As you can see the Neolithic Revolution lead to civilizations.