A bank transfer is a payment that moves money directly from one bank account to another, without cash, cheques or cards. In everyday use the phrase almost always means a payment that the payer starts by telling their own bank to send money to someone else's account, which payments specialists call a credit transfer. The full explanation of how these payments travel and the rules that govern them is in the Credit Transfer entry.
Bank transfers run over different systems depending on where and how fast the money must go. Domestic transfers may use a batch network such as the US Automated Clearing House, an instant system such as Faster Payments in the UK, or a high-value wire. Transfers between countries usually travel as an international wire transfer through correspondent banks.
Because the payer starts the payment, a bank transfer is a push payment; a direct debit, where the payee collects the money, is the opposite case, as explained in push vs pull payments.