Clockrate is the rate that the physical layer is signalling to the other end at. As you'll see below, the clockrate command is only required on the DTE end of a synchronous connection.
If two synchronous devices agreed to send information to each other at an appallingly slow rate of 1 bit per second, then each second, they would sample (listen) to the signal from the other end, and interpret it as a binary one or zero.
Bandwidth is the amount of data, generally in kilobits per second, that you can push through a link. While this is usually a function of the bandwidth value, that may not necessarily be the case. The value of bandwidth is used by higher level protocols such as eigrp and ospf to make decisions about the most suitable link to forward packets.
Asynchronous and synchronous communications refers to the method for clocking data bits. With asynchronous operation, both ends wrap their data with start and stop bits for synchronisation, so effectively clock indepenently of each other. With sync, a clocking signal is sent by one end, and both ends use that signal to time their transmissions.
An async interface, such as a RS232 serial port, has various configurable parameters, such as the number of stop bits, the use of a parity bit, and the length of the data component, but will always send a start bit before the data. A typical standard used for years by BBS systems was 8N1, meaning 8 data bits, no parity, and 1 stop bit. Another common standard, used by older unix machines was 7E1, meaning 7 data bits, even parity, and 1 stop bit. The optional parity bit was used to check for errors at the data link layer.
Both methods meant that 10 bits were used (remember to count the start bit) to transmit 8 bits of data, so for a 9600bps connection, you could get a maximum data rate of 960bits per second, or 120 bytes per second.
With async, there may be an idle period of any length between two successive data transmissions, so for 8N1:
[Start bit][8 data bits][stop bit] --DELAY-- [start bit][8 data bits][stop bit] --DELAY-- ... etc etc
Synchronous communication requires more complicated interface electronics. The data transmitted is clocked to the same signal as the received clock. Because the clock is running continously, regardless of whether there is data to transmit, and because each data packet does not require its own start and stop bits, this method acheives greater efficiency than async operation, and can therefore push more data through the line than async operation can at the same clock rate. In addition, the clock rate can be usually be run faster than asynchronous clocking, giving further performance benefits.
Asynchronous serial ports (these days) typically operate at a maximum speed of 230,400 bits per second. In past years, it was common to see them max out at 115,200 or even 57,600.
By comparison, synchronous serial ports typically run at maximum speeds of 2,048,000 bits per second.
I've been talking about serial communications here, but the concept applies to other technologies too, for example ethernet transmits asychronously, because it transmits an 8 byte (64 bit) preample before each packet for synchronisation purposes.
Disclaimer: Feel free to correct me if I've typed something erroneous, misleading, or just plain wrong
