Fortran is a general-purpose, compiled imperative programming language that is especially suited to numeric computation and scientific computing. This page provides information about Fortran and a link to a page that explains how to use Fortran.
Fortran is a popular programming language for HPC applications. It is very good at doing mathematical operations including matrix operations. There are several built-in routines that have been optimized for the language itself. The name Fortran is derived from the IBM FORmula TRANslator. The language has since dropped the all uppercase requirement. Fortran is still widely used by scientists and doesn't allow as many quirky things as the C language. This keeps the compiler very tight on optimizations. The current standard is Fortran 2008. Nearly all benchmarks done on supercomputers are done with Fortran applications.
You will need a compiler to use Fortran.
View the available compilers on a particular cluster (and the commands they provide) to compile/build Fortran source.