In modern times, there are many reasons for having such festivals. There might be some people who come only to thank the gods for a good autumn harvest, and others who come to celebrate merely for the sake of celebrating. Either is a good reason to host and participate in an autumn festival, but I think it's mostly to have an excuse to hang out with your friends and family, listen to music, eat street food, and play some games.
Historically these festivals arose out of a desire to appease the kami. Japan is often plagued by natural disasters such as tsunamis, earthquakes and typhoons. In the past, people thought these events meant that the gods were unhappy. To try and put the gods in a good mood, people would hold festivals in their honor and give them special treats to appease them. In the case of niiname-sai, people would offer grain from the new autumn harvest to make the gods happy. Aki-matsuri celebrated a bountiful harvest and thanked the gods for their generosity.
