This item is from the Yet Another Enhanced IDE/Fast-ATA/ATA-2 FAQ, by John Wehman and Peter den Haan with numerous contributions by others. (v1.92).
One of the disadvantages of ATA is that it was designed for harddisks only. That was fine back when a high end PC shipped with just a floppy drive and a 40MB harddisk, but today CD-ROM and tape drives are commonplace devices that should preferably run off a single low-cost interface. The ATA Packet Interface (ATAPI) is a standard designed for devices such as CD-ROMs and tape drives that plug into an ordinary ATA (IDE) port.
The principal advantage of ATAPI hardware is that it's cheap and works on on every PC with an IDE or 'EIDE' adapter. ATAPI tape drives can enjoy superior performance and reliability compared to the popular QIC117 'floppy' tape devices.
Beware that although ATAPI devices plug into the IDE interface, they differ considerably from an IDE harddisk. Caching controllers and other intelligent interfaces will not work unless they're ATAPI aware. Booting from an ATAPI CD-ROM is only possible with the latest BIOSes.