CIA stands for Complex Interface Adapter, and there are two CIA chips inside each Amiga computer.

The CIA chips enable the parallel port, serial port, provide timers, interrupt signals, joystick and other interfaces which are not provided by other chips within the machine.

The Amiga computers used the 8520 CIA chips, which were a later revision of the 6526 CIA chips, also used in the Commodore 64 and other machines and peripherals using a 6502 CPU.  The main difference was that the later revisions in the Amiga used a different method to calculate the time of day timers.