''Transaction Signing'' means in this context that the transaction data are shown to the user on the smartphone a second time and the user confirms the transaction via OK. Internally, the transaction data are hashed via the secret key.
The starting point in 2007 for the development of eKaay was an online banking method, i.e. a transaction signing method (that time with J2EE applets). In the meantime eKaay became a log-in method. Nevertheless, the transaction signing functionality is still built in. It can be used for example for low-value payment, see this demo page:
Here you find the demonstration of the original online banking method: