The 8255A Programmable Peripheral Interface chip has two main modes of operation - I/O mode and Bit Set-Reset mode. In I/O mode, the ports work as programmable I/O ports and can be configured in three sub-modes (Mode 0, 1, and 2) using a Control Word Register. Mode 1 uses handshaking signals to coordinate data transfer between ports. Mode 2 allows bi-directional communication on a single bus. In Bit Set-Reset mode, individual bits of port C can be set or reset using the Control Word Register.