Ethereum is not just a history of blocks. It also has a current state: the latest version of who owns what and what each account stores.

Blocks contain transactions. Transactions update state. When Mark sends Jalil 1 ETH, Ethereum records a new state where Mark has less ETH and Jalil has more.

Nodes replay and verify the same blocks so they can agree on the same current state. This is why Ethereum can keep one shared record without one central server.