The MPI (Message Passing Interface) is a language-independent communications protocol used to program parallel computers. It allows many computers to communicate with one another. It is used in computer clusters.
The OpenMP (Open Multi-Processing) is an application programming interface (API) that supports multi-platform shared memory multiprocessing programming in C/C++ and Fortran on many architectures, including Unix / Linux and Microsoft Windows platforms. It consists of a set of compiler directives, library routines, and environment variables that influence run-time behavior.
This tutorial explains how to obtain, build, and use an MPI stack for Linux machines. This tutorial will take you from "hello world" to parallel matrix multiplication in a matter of minutes. The exercise takes slightly more than 30 minutes and allows one to develop and run MPI codes on a multi-core server or on a HPC cluster.
OpenMP has several strong points: it is a very simple system to use and it is widely available in compilers for most major platforms. There are however, other methods to express parallelism in your code. On distributed parallel systems, like Linux clusters, the Message Passing Interface (MPI) is widely used. MPI is not a programming language, but rather a standard library that is used to send messages between multiple processes. These processes can be located on the same system (a single multi-core SMP system) or on a collection of distributed servers. Unlike OpenMP, the distributed nature of MPI allows it to work on almost any parallel environment.