Where to begin... You're right, SCSI (Small Computer Storage Interface is what I believe it stands for) is storage interface, much the same as IDE and SATA (not RAID though). Without getting into the very technical differences, its just another stage interface and as such requires three things to run on a common computer.
1. SCSI interface card. You can add in a PCI card and/or some motherboards have SCSI interfaces built in (usually higher end workstation/server boards for example)
2. SCSI cable. This is obvious but a specific cable is necessary.
3. SCSI HDD. The actual harddrive must have a SCSI interface.
Now, Phisically/Technically, there is no difference between SCSI hard drives and IDE/SATA... they are all the same. The only difference is in the interface. So, in saying that SCSI hard drives are faster, this is actually not becaue they are SCSI but more because SCSI is usually used in high-performance conditions and most SCSI hard drives are geared towards that. Also, people who buy SCSI (corp. america) is use to spending large (relative) amounts of money on storage and new (read: fast) technology is always more exensve... again, leading to SCSI drives being faster.
There are many levels of SCSI (U160/U320 for example)... think of them as versions of ATA (66/100/133) in that each supports a higher amount of theoretical throughput. Also, SCSI can support 15 devices per channel unlike IDE (and even SATA which is point to point single device).
Anyway, this is just a rough explanation... if I've missed something I'm sure someone else will add.