An instance is a single "instance" or "endpoint" of a Realm Object Server. It can synchronize data between client-side application bindings. It's also the core metric around Realm pricing model seen here: realm.io/pricing . By default, the standard cloud plan allows three instances. Most of our users segment these as development, staging, and production though there is no requirement.
It is a common misconception to think that each application user will need their own instance of the Realm Object Server due to privacy concerns. A single server instance is used to serve many, many clients. Realm allows ACLs to be set which can segment your users' data so that their privacy is maintained. For more details, see: Realm Sync Docs: Access Control.