Hi Jabbar,
Basically Parellel is sending 8 bits at a time and serial is sending one. There is some overhead in the parallel port which results in an aproximate 5x faster connection for parallel as compared to serial.
The data rate used on parellel port comminications is typically tens of kilobytes to few hundred kilobytes per second.
In serial, asynchronous data transfer the individual bits which comprise each data byte are sent one after the other over a single line. There is one wire for data transmitting and one for data reception. In addition this there are several status/handshake lines. In this context, asynchronous means that the clock information is not included with the transmission, so that frequent re-synchronization using start/stop bits is required.
Hope this will provide you the basic difference between the two.
Rate if it does,
Rgs