Github is a frequently used service in the toolbox of API owners. The most common use of Github is for publishing API SDKs in a variety of languages and platforms. But when it comes to truly being an "open API", some API owners are actually open sourcing their API design using Github.
Open sourcing the design of your API will not be sensible for every provider. Many companies are looking to ensure developers use their API, maintaining an advantage over competitors. However in some cases, open sourcing the design of your API is a way to ensure interoperability between partners or among mutliple companies within a certain business sector.
Simple examples of an API design might be for common systems like blogs, news, links, calendars or other API designs that don't deliver any sort of proprietary offerings. If you are looking to ensure synchronicity between say, the calendar of multiple organizations, developing a single API and open sourcing the design and possibly a version of it in multiple programming languages, might make sense.
With a consistent API design, and code to deploy the API, any organization can download or fork the Github code, deploy the API for themselves--ensuring consistency and interoperability between any deployment. If a single organizations has unique needs, they can extend and commit the code back to Github, allowing the central repository manager to decide if it is a change that should be added to the core offering.
Not all APIs are created equal. Consider the possibility of actually open sourcing your API, the benefits it might bring to others, as well as your organization--they might exceed keeping it closed and proprietary.
This approach to using Github, is by far the truest meaning of the word, "Open API".
