I think I understand these concepts but I'm a little rusty. Can someone give a concise, easy-to-understand explanation of these concepts? The planes are logical concepts, correct? Is this a cisco only thing?
These terms are abstract logical concepts, much like the OSI model.
Data plane refers to all the functions and processes that forward packets/frames from one interface to another.
Control plane refers to all the functions and processes that determine which path to use. Routing protocols, spanning tree, ldp, etc are examples.
Management plane is all the functions you use to control and monitor devices.
These are mostly logical concepts but things like SDN separate them into actual devices.
Finally, all manufacturers use these concepts.
Forwarding Plane - Moves packets from input to output
Control Plane - Determines how packets should be forwarded
Management Plane - Methods of configuring the control plane (CLI, SNMP, etc.)