From Unofficial BOINC Wiki
The class of those computers that are the fastest and most powerful computers available at that time. Today's supercomputer is tomorrow's desktop machine. This class of computer is used for intense scientific processing. The architecture of these machines is shifting from the single high-speed processor systems to clusters of less expensive off the shelf components connected with high speed networks. One of the more recent machines was built using 5,000 some odd Apple dual G5 computers.
At any given time, that class of "general purpose" and "purpose-built" (those machines designed to solve specific problems, or classes of problems) computers that are in general both faster than most of the computers in the lower next tier of computing power and have sufficient central memory to store the problem sets for which they are designed. Computer physical and virtual memory spaces are larger, input-output throughput, computational rates, and other related computer capabilities contribute to this higher level of performance. As a consequence, a quantitative measure of computer power in large-scale scientific processing does not exist, and a precise definition of supercomputers is impossible to define.
One of the prime distinctions of a supercomputer and a mainframe is that in general, the application domain of the supercomputer is in science and mathematics while the mainframe is dominate in the realm of business process support.
Lastly, today's supercomputer is tomorrows PC.