Mainframe is an industry term for a large computer. The name comes from the way the machine is build up: all units (processing, communication etc.) were hung into a frame. Thus the main computer is build into a frame, therefore: Mainframe.
Mainframes have huge processing and storage capacity. The development cost involved with mainframes is also very huge and therefore mainframes are manufactured only by very large companies. Mainframe gets its usage and applications in banking and financial sectors where large-scale operation with millions of records per day is involved.