Microsoft describes Graph as "a RESTful web API that enables you to access Microsoft Cloud service resources." So if Graph is just a Web API, then why does Microsoft make such a big deal out of it?

Microsoft CEO Satya Nadella called Office Graph Microsoft's 'most strategic API' back in 2014. But it's only now that Microsoft watchers are seeing tangible evidence of the clear implications of ...

Graph offers an application programming interface (API) that developers use to connect to a wide range of data — email, calendar events, files, etc. — across Microsoft cloud services.

Basically, the Open Graph API is a way for Facebook to allow other companies, sites, services, etc to interact with Facebook without having to create a dedicated Facebook Page.