Different architecture. As /u/DeHackEd notes in great detail, exactly what a modern supercomputer is doing differently depends on which one you’re talking about, but they all share the fact that they’ve got a different architecture than a typical PC that allows them to do some factor (or more) to a *far* higher/more scaleable degree.
That many mean thousands of processors in parallel, that may mean terrabytes of RAM, that may mean petabyte disk arrays with the associated high bandwidth connections, that may mean massive parallelism like Folding@Home, but it means something about it is orders of magnitude higher performance than any typical single computer.
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