When using the Marbles tutorial, there is a “Story Mode” option that will display more details about the transaction process.
See point 10 under the “Use Marbles” heading. Transactions are stored on a ledger which is associated with each peer. Refer to the Hyperledger Fabric documentation on the ledger. The linked Transaction Flow section might also be helpful. The ledger itself is not propagated to a client-side application. However, queries initiated from client applications can be run against the ledger to return information. The Hyperledger Fabric Writing Your First Application documentation topic could also help to explain how querying the ledger works.