A transaction authentication number (TAN) is a one-time password that is usually made up of six decimal digits and is used in online banking. The TAN is currently sent to you by SMS and is valid for two minutes.
In addition to your login credentials, a TAN serves as a second security layer. If someone has access to your login credentials, they cannot log in without a TAN or carry out a transaction later. The same applies the other way round: if someone has your TAN, they will need your login credentials to log in and later a second TAN to carry out a transaction.