The auto announce button toggles between two different forms of announcing auto note switches.
When an auto note switch occurs, it is important that you know that it has occurred. Otherwise you may be trying to tune with the wrong note selected. When auto announce is enabled, VoiceOver will speak the newly selected note name and octave whenever the selected note changes. Unfortunately the system also mutes the whooshing tone for several seconds when VoiceOver speaks this announcement, which can be a nuisance if you don't want to wait that long to start tuning the new note.
As an alternative, you can have a shorter announcement that does not use VoiceOver. Instead it consists of several beeps that are mixed in with the whooshing tone when the note switch occurs. This occurs in a fraction of a second and does not mute the whooshing tone.
The button that selects between these two options is on the Settings screen. When selected, this button reports either "Auto Announce is On" or "Auto Announce is Off". Activating this button toggles between these two options.