What is the difference between wireless controllers and access points, and how come you need both devices to work efficiently together?
The controller function (not necessarily a dedicated device by the way) is essential to how any wireless network bigger than what you have at home works.
- It allows you to configure large sets of APs efficiently from a single point
- It manages the APs' radio layer such that the APs work together as a whole without interfering with each other
- It may provide a termination point for traffic which needs to be tunneled up to a central point and filtered through a firewall (typically guest traffic for example)
- By centralizing the "intelligence" of the wireless network it theoretically allows for simpler and cheaper APs (hence the "Lightweight" par of LWAP), though honestly I'm not sure to what extent this is still true.
In the Cisco world all that gets handled by the WLC, usually as a set of physical appliances, but there are other manufacturers which split this up, such as Aerohive, where the config server may be in the cloud, the radio management part is handled in peer-to-peer fashion by the APs themselves and you can get a sort of vpn gateway for tunneling traffic back to a central point.
A WLC will control all your LWAPs. You can control all the aspects of the LWAPs from the WLC. Normally, your LWAPs will create a CAP/WAP tunnel back to the WLC, and the Wi-Fi traffic will traverse the tunnel back to the WLC, where it will be put onto the network.