The InstitutionId is a logical partition field we use to allow multiple, independent sets of data related to campuses, sections, courses, etc. to live in a single DB instance. We use the term "multi-institution" to describe the scenario. This is setup at install time. It is placed in the web.config of the web server as well as some other places. Institutions can be added later if necessary.
To look it up, you actually look in the Organizations table (for historical reasons).
If you have only one Institution in your system, you can look up its Id like so: