The MonoBridge is a system that makes sure every GameObject is linked to its networked representation. It essentially interfaces between the GameObject world and the coherence SDK code running "under the hood".
When you place a GameObject in your scene, the MonoBridge detects it and makes sure all the synchronization can be done via the CoherenceSync component.
At runtime, you can inspect which Entites the MonoBridge is currently tracking.
A MonoBridge is associated with the scene it's instantiated on, and keeps track of Entities that are part of that scene. This also allows for multiple connections at the same time coming from the game or within the Unity Editor.
When using a Global MonoBridge (Singleton), the MonoBridge is still associated to the scene it was originally instantiated on, even when the GameObject deattaches from the scene and becomes part of DontDestroyOnLoad.