IBM Disc Electronics or Integrated Drive Electronics is more commonly known as ATA or Parallel ATA (PATA) and is a standard interface for IBM compatible hard drives.
Every computer needs special circuits to control the hard disk, either on an add-in board plugged into an expansion slot, or circuits built right into the computer's main motherboard. In the PC world, there are several different standards for these controller circuits, including ST506,ESDI, and SCSI. But these days the most common type is called IDE (for integrated drive electronics or ). In practice, all of them are equally fast. IDE wins because it's simple and inexpensive.
Still, the main thing to remember is that your hard disk has to match the controller-if you have an IDE controller, you need an IDE hard disk, and vice versa. On the other hand, if you're buying a new hard disk for an old PC that has an ST506or ESDI controller, you need that type of hard disk instead (or you have to buy a new controller too). SCSI hard disks and controllers are relatively complicated and expensive, so don't bother with them unless you really need SCSI'S special capabilities (such as disks bigger than 600 megabytes, and the ability to hook up other types of devices, like CD-ROM drives, in series with your hard disk).