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Message Passing Interface (MPI) is a defined interface, both a program library interface and a communications protocol for passing data between the processors of a multiprocessing system. Carrying out a large computation taking advantage of a modern multiprocessor (e.g., with thousands of processors) requires figuring out how to order the computations, and getting the right data to the processor in order for it to continue its part. MPI provides the means to move data from processor to processor, so that programs written to use it have the opportunity to use the processors to complete a computation more quickly. It requires an underlying means to move data, and defines the protocol so the programming at both ends cooperate in the transmission of their data.
Note that the abbreviation MPI is also used within astrophysics for the phrase Max Planck Institute, e.g., the Max Planck Institute for Astronomy (MPIA).