Serial and parallel ports are to different types of connectivity device. They can be used to connect all types of peripherals like modem, mouse and printers. The major difference between serial and parallel ports is that serial ports transfer data one bit at a time while parallel ports can transfer data eight bit or more at a time. Serial ports have to take a part the eight bit in a byte and transfer them one by one. On other hand, the newer parallel ports line up the eight and can transfer them all at once.
Because serial ports can only transfer data one bit at a time so it is much slower than parallel port. But serial ports require fewer wires. This is because parallel ports need eight wires to be able to transfer all eight bits at one time. Serial ports are much cheaper than parallel ports.