From LQWiki

A Mainframe (also called big iron, or, historically, a minicomputer) is a really big server computer. Mainframes have a cost that typically starts in the hundreds of thousands of dollars/euros and can expand well into the millions. Companies such as IBM, ICL/Fujitsu, and HP have been noted for their mainframes. IBM have notably been at the front of selling people SuSE Linux-running mainframes. Mainframes are noted for their stability, and they support vast numbers of users. They are used by banks and large security-conscious or data-hungry projects. An interesting fact about mainframes is that they run really hot; older mainframes are used to heat the office buildings that they surround. They are usually kept in clean rooms and/or data centers. The name "mainframe" comes from when this class of computer was first introduced, in the days of room-filling dinosaurs. An entire mainframe computer could fit in the main frame, or cpu rack, of an older computer.

There is an ongoing holy war fought out between people that say you should have very large, reliable fast and expensive mainframes running things, and those that say you should have clusters of slower, less reliable, much cheaper computers which you swap out when they go wrong. It's been raging for a very long time, and it probably comes down to a difference of style - thanks to Linux, you can run a whole cluster of computers that act like a single machine, or you can run one mainframe that acts like a hundred machines (or even a cluster of a hundred machines). (See Beowulf.)

People that use and run mainframes often comment that desktop PCs are just discovering techniques and features that mainframes already had 20 or 30 years ago. They are often referring to things like multi-tasking, multi-threading, multi-user and virtualization aspects of operating systems, but then again, there are digital wrist watches now that have more RAM than old mainframes did in the 60s.

A Mainframe can also be contrasted with a Supercomputer.