You have several components. First, there is the line rate. This is a fixed maximum that you cannot exceed per timeslice of the circuit. If it is 128000bps, there is no way to put more than that on the circuit. If there is an arrangement in place, or you want to shape some of your traffic to an average of 64000bps, that would be your CIR (64Kbps). That leaves a couple of things sort of up in the air.
First of all, a second is an eternity on a circuit. So with a CIR or 64Kbps, should traffic be sent at full throttle for a half a second, then none for a second. That could cause issues with most interactive traffic, especially voice. So what we need to do is break the 64000 down into smaller chunks and transmit them more regularly. We may choose to break it down into 8000bit chunks. This 8000bit burst (Bc) means that we would transmit these chunks at every .125 seconds (still not small enough interval for voice). This is Tc or the time interval.
Now we know that there is still room on the circuit to transmit another 8000 bits per .125 seconds. Suppose that we had not transmitted anything in the last 5 timing interval. Let's also say for example that we have an excess burst of 24000. Of the last 5 timing intervals, we could have sent 40000 bits, but we sent zero. We have a Be (excess burst) of 24000. These 40000 bits fill the Be token bucket to capacity and spills over. The total capacity is again 24000 and this bucket is now full.
Now assume we have a 50000 bit chunk of data that arrives to be transmitted. Per each timing interval, we have 8000bits that we can transmit from the regular burst and we can begin using the 24000 bit credit we have in our excess burst token bucket. Since the line speed is 128000 or 16000 per Tc (timing interval), we have the headroom to use up to 8000 of our Be tokens per interval. In other words, we can transmit 16000 bits (8000 Bc + 8000 Be) for three timing intervals then sustain 8000 (Bc) there after. When our traffic stops in the future for three intervals our Be token buck will be full once again.
So our 50000 bit chunk of data will drain our Be token bucket in 3 intervals. By the end of the third interval it will have transmitted 48000 bits of data and only 2000 will remain in the queue. This is a queuing example, but policing works in a similar manner.
This is a difficult concept to grasp. Sometimes, one person's way of explaining may make more sense to you than another's. So if this is still confusing read plenty of examples and you'll get it. Also post back with additional questions and I'll try to help clarify.