The application data graph is a fundamental concept in modern applications, where data can be represented as nodes and edges. GraphQL allows us to extract trees from the app data graph by defining root query types that specify where a query can start when traversing the graph. The tree structure of GraphQL lends itself well to client-side caching, with Apollo Client using assumptions such as "same path means same object" to reduce roundtrips to the server and improve application performance. Object identifiers are used to identify unique pieces of information in the app data graph, allowing for more efficient caching and updating of query result trees. By understanding these concepts, developers can leverage GraphQL and Apollo Client to build fast, snappy applications with improved reactivity and caching capabilities.