Loopback can be run on both the client and the server using isomorphic LoopBack. The same app running in NodeJs can also run in the client browser so instead of coding HTTP requests and responses on the client to CRUD your LoopBack model instances, you can simply call the appropriate loopback method.
In other words, instead of calling a POST to an API end-point to create a new object (POST /api/MyObject) in your database, you can simply call MyObject.create(data) on the client and the LoopBack app in the client will make the call for you. And instead of returning an HTTP response, it will return the created object.
Now, this brings us to the difference between /common and /server models: if you want the model used in the browser to be the same as the model used on the server, create your model in /common. If you need the model to be different, create the model in the /server/models folder (not sure where to create the model for the client)