Forwarding Rate tells the number of packets/frames processed and sent out of the switch.
Forwarding bandwidth is also reffered as Uplink bandwidth. The traffic moves from acess layer switches to distribution layer switches will more compared to the individual traffic on the access layer links. Usually these uplinks will be of higher capacity than the rest of the ports in a switch. E.g: If a switch has 24 100Mbps access ports, it will be having 2 1000Mbps uplink ports.
Backplane is the bus present in switches for transferring data between its ports. The speed of the backplane bus will affect the forwarding rate of the switch.