According to Diamond, agriculture gives more people more time to do things other than get food. This allows them to do things that can be seen as developing culture.
Hunter-gatherers must (in general) all work at getting food almost all of the time. This means there can be no specialists in such societies. There cannot be people who make a living as artists or singers or storytellers. With farming comes surplus food. Many people do not have to spend any time getting food. This means they can specialize in other professions. Some of these will have to do with culture. Thus, agriculture allows people to have enough food so that some people can do things that help to create culture.