Monitor Setup in Ardour
Ardour has three main settings which affect how monitoring is performed. The first is Edit > Preferences > Audio > Record monitoring handled by. There are two or three options here, depending on the capabilities of your hardware.
The other two settings are more complex. One is Tape machine mode, found in the same dialog, and the other is the Session > Properties > Monitoring automatically follows transport state setting.
Monitoring also depends on the state of the track's record-enable button, the session record-enable button, and on whether or not the transport is rolling.
Software or Hardware Monitoring Modes
If Ardour is set to external monitoring, the explanation of Ardour's monitoring behaviour is simple: it does not do any.
Monitoring in Non-Tape-Machine Mode
When Tape-Machine mode is off, and a track is armed, Ardour always monitors the live input, except in one case: the transport is rolling, the session is not recording, and auto-input is active. In this case only, you will hear playback from an armed track.
Unarmed tracks will play back their contents from disc, unless the transport is stopped and auto-input is enabled. In this case, the track monitors its live input.
Monitoring in Tape-Machine Mode
In Tape-Machine mode, things are slightly simpler: when a track is armed, its behaviour is the same as in non-tape-machine mode.
Unarmed tracks however will always just play back their contents from disk; the live input will never be monitored.