LINPACK is a computer benchmark used to rank supercomputers, most notably for the well recognized "TOP500" list maintained by the University of Mannheim and the University of Tennessee.

Originally devised and designed by Jack Dongarra, LINPACK consists of a highly parallel algorithm for solving a system of linear equations. It is recognized as being a good representation of a given computer's dedicated processing power for solving the typical problems that are run on supercomputers -- namely, simultaneously solving numerous equations with floating point values.

For more info:
http://www.top500.org/lists/linpack.html
http://www.netlib.org/benchmark/performance.ps (a VERY long report by Dongarra)

LINPACK is also the LINear algebra PACKage, a now obsolete set of libraries primarily for UNIX and UNIX-like operating systems. It was used for efficiently performing linear algebra calculations, most notably on the large machines which were benchmarked using the above-mentioned software. It has since been replaced by a more efficient, versatile and functional suite called LAPACK.