From The RadioReference Wiki
A controller is the brains behind any trunked radio system. "Controller" is a generic term that refers to the computer system that tells radios which frequency to use for a conversation at any given time. The controller listens, and talks, on the control channel at a trunking tower site, accepting channel grant requests from radios, and sending out instructions to the fleet.
In multisite trunking, controllers at multiple towers will communicate with one another to complete users' radio calls.