Mohammad,
Switch C receives an inferior BPDU (meaning a worse BPDU) on Fa0/16. This worse BPDU was created by Switch B because after Switch B’s link to Switch A went down, Switch B now believes it is the Root Bridge. Since it is the job of the Root Bridge to create BPDUs, Switch B is doing what it thinks is the proper activity. However, Switch C knows that Switch B is mistaken. It knows this because Switch C is still able to receive superior BPDUs (meaning better) from the true Root Bridge, Switch A.
Bridge ID is determined by a combination of Priority and MAC Address. The lower the Bridge ID, the better–as far as being elected as the Root Bridge. Since in this example all switches have the same priority, it is the MAC address (the lowest MAC) which determines the Root Bridge. Switch C sees BPDUs coming from “BBB” and from “AAA” both claiming to be root. Switch B knows that AAA is lower than BBB, so it ignores BBB.
After 20 seconds of not receiving any more BPDUs from AAA on its port Fa0/16, Switch C transitions from Blocking to Listening to Learning to Forwarding. Only after all that happens (50 seconds, maximum), will Switch C send an “AAA” BPDU to Switch B. It is at this point that Switch B realizes its mistake (that it shouldn’t have claimed to be the Root Bridge). During this entire 50 second process, user data cannot leave switch B, so there would be an outage. Backbone-Fast is meant to minimize this outage.