WebThings Gateway is an open source project maintained by a community of volunteers.
The API exposed by the gateway is called the Web Thing API. We are currently in the process of migrating this API to conform with W3C Web of Things standards. You can see an overview of differences between the two here.
WebThings Gateway has a directory of community-contributed add-ons which enhance its capabilities.
To learn how to develop your own add-on or contribute to an existing one, you may want to start with the resources below: