A TAN (Transaction Authentication Number) is a OTP (One-Time Password) sent to a user which they will enter in to their mobile banking application to authorise a payment. This OTP is sent either via text message, email or as a pop-up message alert, depending on how the banking application is set up.
TAN Numbers are used as a secondary form of 2FA (2-Factor Authentication) which helps to secure a bank account. This prevents against fraud, and ensures that only the user with access to the paired device, email address or phone number will be able to validate the access.
TANs are one-time codes, meaning that they can't be re-used. There is typically a short time period where a TAN is valid, after which point it will expire and no longer be used.
TANs are mostly used in the EU, and specifically in Germany, although adaptation is being expanded in other countries.