FlexConnect is one mode an AP can operate, typically deployed in Branch setup where you do not have a controller at branch site. Those AP can register to a controller at your HQ or main site. So traffic will terminate at your branch switch instead of tunnel back to HQ-WLC.
If you want roaming within your branch FlexConnect AP then you have to put those AP into a FlexConnect Group. Then only key information shared among those AP to facilitate fast roaming.
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FlexConnect Group feature is basically used to organize and manage your FlexConnect access points, you can create FlexConnect Groups and assign specific access points to them.
All of the FlexConnect access points in a group share the same backup RADIUS server, CCKM, and local authentication configuration information. This feature is helpful if you have multiple FlexConnect access points in a remote office or on the floor of a building and you want to configure them all at once. For example, you can configure a backup RADIUS server for a FlexConnect rather than having to configure the same server on each access point.
Since (at least) 7.6 AirOS code you can also specify WLAN ID <-> SSID ID mapping for the local switched SSID's in the flex-connect groups, so you don't need to do that on the access-point locally anymore :-) .