The Open Source Initiative (OSI) is a non-profit corporation dedicated to promoting the idea of Open source, basically an Open Source advocacy group.
OSI is aimed especially at business and other pragmatic users, therefore it emphasizes less the freedom aspect of Open Source / Free Software and instead focuses on the value OS can deliver.
One important project of the OSI is the OSI certified certification for licenses. This certification, born from the Debian guidelines, makes sure that a license meets certain basic requirements with respect to openness.
OSI is in a way a pragmatic counter-movement to the more dogmatic (some would say more radical) position of the Free Software Foundation. In particular, Richard M. Stallman hates the term Open Source, as he believes that the term makes people forget about the important issue of freedom.
Note: see the node on open source for a more extensive discussion of the difference between the concepts of Open Source and Free Software.