Your wallet (which is a collection of Bitcoin addresses) acts somewhat like an “account” but there is no actual “account” in the database. For most users all it is enough to know the wallet acts as the account “manager” and maintains the “balance.”
When transactions are made there are “Inputs” and “Outputs.” If you have 10 bitcoins in your wallet and you send 1 to someone else you have 2 Outputs, 1 bitcoin and 9 bitcoins. The 9 bitcoins goes to another address in your wallet and it is called “change.” After many of these transactions the database a series of Bitcoin addresses with unspent inputs. You wallet programs scans the blockchain and adds up all the unspent “Inputs” for each address in the wallet. The wallet contains the “private keys” for each of the Bitcoin addresses. The unspent bitcoins can only be spent with the private key. If you run a wallet locally it takes awhile to start (even if the Blockchain is fully loaded) because these balances are being calculated by scanning the Blockchain.