A mid-range class of computer falling between a mainframe and a personal computer (not room-sized but are too large to fit on a single desk). Minicomputers were very popular during the 60s, 70s, and 80s as multiuser machines for academic, office, and industrial use.

DEC produced the world's first minicomputer, the PDP-1, in the early 1960s. The company followed with an entire line of machines, culminating with the popular PDP-11 and, later, the famous VAX architecture in the late 1970s. Other well-known manufacturers include IBM (with the AS/400 and RS/6000), Hewlett-Packard (with the 3000 series), and Data General (with the Nova).

Modern-day computing owes much to the minicomputer era. PCs are direct descendants of minicomputers hardware-wise, and many popular PC applications such as the word processor began life as minicomputer apps. The Unix community in particular owes much of its heritage to these machines. It is said that Ken Thompson originally invented Unix in 1969 so that he could play games on his PDP-7. Thereafter the Unix platform flourished in the guts of PDP-family machines and VAXen.

In recent years, however, the term "minicomputer" has fallen out of common usage. As PCs have become more powerful and have gained advanced multiuser capabilities (thanks in large part to x86 flavors of Unix), the distinction between PCs and minicomputers has become blurred. Today, machines working in traditional minicomputer roles are commonly classified simply as servers or workstations.


Sources:
http://www.wikipedia.com/wiki/Minicomputer
http://wombat.doc.ic.ac.uk/foldoc/foldoc.cgi?minicomputer
The Jargon File