Yes, multiple access points can be connected to a wired LAN, or sometimes even to a second wireless LAN if the access point supports this.
In most cases, separate access points are interconnected via a wired LAN, providing wireless connectivity in specific areas such as offices or classrooms, but connected to a main wired LAN for access to network resources, such as file servers.
If a single area is too large to be covered by a single access point, then multiple access points or extension points can be used. -- Note that an "extension point" is not defined in the wireless standard, but have been developed by some manufacturers. When using multiple access points, each access point wireless area should overlap its neighbors. This provides a seamless area for users to move around in using a feature called roaming.
Some manufacturers produce extension points, which act as wireless relays, extending the range of a single access point.
Multiple extension points can be strung together to provide wireless access to far away locations from the central access point.