Online Banking
In short: Online banking is handling banking business via the internet or an app.
In more detail: Customers check balances, transfer money and manage standing orders.
In Depth
Security
Since the EU Payment Services Directive PSD2, strong customer authentication is required: two factors from knowledge, possession and inherence (MFA). Common methods: pushTAN app, chipTAN with card reader (card readers), fingerprint in the banking app.
Dangers
Phishing, banking trojans, social engineering. See vishing.
Interface
Banks offer FinTS/HBCI as a standard interface for programs. See PayPal.
See also: MFA, Banking Trojan, Phishing, PayPal