The blockchain is the Bitcoin network’s shared transaction record, and all full nodes and miners keep their own copy of it. This ensures all users are always in agreement about who owns what (in other words, the state of the UTXO set). Agreement on which blockchain is the correct one is ensured through Bitcoin’s consensus rules.
One of the main consensus rules is that the correct blockchain is the chain whose transactions are all valid and whose blocks have the most accumulated Proof-of-Work. As long as all users have the same blockchain, and are operating under the same protocol, they will all independently arrive at the exact same state of bitcoin ownership (again, the UTXO set).