The Backplane represents the internal switch bandwidth (the maximum amunt of data that the switch can handle (internally),
The Control Plane usually refer to packets destined for the router (Routing Protocols - where we move the data / ssh / telnet / snmp, etc)
The data Plane refers to the actual moving of the data.
Control plane functions refer to processes that are run in software, whereas data plane functions refer to processes that are run in hardware (ASIC).
For backplane pl check below documents, in very depth explanation.
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"Backplane" is a term that goes way back. It refers to the main chassis hardware into which you insert other cards. It's the chassis hardware that "glues" together the inserted cards so they can communicate with each other. The backplane, besides providing intercard data communication also generally provides power to the inserted card modules. So, the backplane generally has control connections, data connections and power connections. The backplane might being totally passive, i.e. is just provides the wiring between cards, or it might be active, i.e. has some supporting "intelligence".
"Control Plane" and "Data Plane" are logical constructs that address a device's control functions and its data forwarding functions. In a backplane, as noted above, there are control connections and data connections, but they may share the same physical connections or not. Also physical connections used to generally run over "buses", and still might, but now there may be multiple buses and/or data connection might run over a "fabric". In other words, there are lots of variations for hardware, but "Control Plane" and "Data Plane", again, avoid the hardware variations and just consider the logical functions. Also, "Control Plane" usually addresses a higher level of intelligence than backplane control.