Depends on where the applications are located. But you are essentially correct - during a failover, the SQL Server stops on one node and starts on a new node. This will close all existing connections, and roll forward/backward all open transactions.

Some applications can be coded to be "cluster aware" and thus handle this situation. Other applications will just reconnect without a fuss.

If an application expects the database to always be available, and has little or no error handling which runs when the database fails to respond for a few seconds, then that application will probably throw a nasty error.

Andy