The term became common in the late 1990s, describing a problem particular to Iomega's Zip drives. Zip disks, although popular, were not particularly sturdy (being exposed to the dust and grime of an unfiltered environment), and the drives were prone to developing misaligned heads. These damaged and dirty heads would try to read a disk, only get a marginal signal, then the controller would quickly snap the head arm back into the drive and out again, producing the "click" and (in many cases) tearing up the edge of the disk and even the heads themselves. Compounding the problem, the damaged disks would often go on to damage the heads of any other drive they were used in.
Iomega received thousands of complaints about the click of death, but denied all responsibility: often, to the fury of Zip drive owners, claiming that the problems were caused by the use of (functionally identical) third-party media. A class action suit was filed against them in September 1998. The case was settled in March 2001 and Zip drive owners were given a rebate, but Iomega's reputation has yet to fully recover.
On non-Zip systems (usually a hard disk), the click of death refers to a similar phenomenon; when a hard disk has a hard error or servo failure, the head actuator will buzz and click as the drive tries to recover from the error. Since the media is not removable on these drives, the defect is almost always due to physical abuse or a manufacturing error. IBM's storage division had their own click of death problems in 2001 with the mass failure of their popular Deskstar 75GXP hard disks.