Scaling can be thought of using Agile from a few Agile teams to multiple, or even hundreds of Agile development teams. There are some unique challenges that come up whenever you have an organization where more than few Agile teams need to work together in a coordinated fashion. Larger Scrum projects scale by having multiple Scrum teams rather than having one very large Scrum team.
Here is a scenario where there is a single Product Backlog from which the individual team backlogs branch out.
In such an environment where there are multiple teams working on a product, it may not be feasible to have one individual playing the Product Owner role. In this situation, one possible solution is to introduce the role of a Chief Product Owner. A Chief Product Owner is responsible for the overall product, guides the other Product Owners, and facilitates the product decisions. The Product Owners and the Chief Product Owner need to work very closely with each other to synchronize with respect to the priorities and dependencies across the teams. However the frequency of coordination depends on the nature of the project/product/organization.
There could be another Scenario where the Product Backlog is divided into different Area backlogs and we have Areas teams working on specific Area backlogs. The Chief Product Owner (CPO) and the Area Product Owners(APO) coordinate to synch up on the Area backlog level priorities. The Area Product owners could in turn coordinate with the individual team Product Owners working in that specific area.
The hierarchy of Product Owners and the Product Backlog depends at large on the context and the nature of the product and organization. The teams in a scaled environment may choose to do joint Sprint ceremonies depending on the amount of common backlog items and dependencies they come across.
Scrum of Scrums and Meta Scrum are the commonly used ceremonies that are used to coordinate across multiple teams in a scaled environment.