An Acronym for Small Computer Systems Interconnect.
An electrical standard for attaching peripherals to a computer motherboard as well as a communication Protocol between devices, generally considered more reliable than IDE/ATAPI. Devices tend to be palpably more expensive too.
SCSI used to be far more sophisticated than ATAPI. F.ex, SCSI pioneered asynchronous command operation -- that is, the host could send a read or write request to a device and go on its merry way, only coming back to collect the data when the device finished reading or writing. In contrast, sending a command to an IDE device meant waiting while the data or a success confirmation was being delivered. Over time, though ATAPI (the IDE communications protocol) has been becoming ever more SCSI-like.
The SCSI protocol requires a host card (called an adapter). SCSI peripherals are then attached to this card. In theory (ha!) up to 127 devices in one chain can be attached to each host card. SCSI cables require a special terminator at each end.
People sometimes describe SCSI as requiring black magic (including sacrificing a goat's blood, or occasionally Lusers).
Note: Do not underestimate the black majick involved in SCSI! If you don't have a terminator on the non-controller end, it might work for a while, and then never work again. Or it might work under some OSs but not others. Put a terminator on it already. While you're at it, ensure both ends of each channel are terminated. Most modern cards have "Auto" termination, and this almost always works these days, but if unsure, set to "Enabled", terminate the end of the cable, and if you're unsure if your cable terminator is active or passive, enable "term. power" on at least one of the devices on the channel.
The SCSI instruction set for controlling devices or a subset thereof is used in some non-SCSI places -- for example, the aforementioned ATAPI, or the "mass-storage" USB device class (which is why you need mod_scsi and scsi_generic support in the LinuxKernel for USB mass_storage support).