When you load an audio clip into a trigger slot, Ardour applies some heuristics to estimate its tempo in beats per minute. Unless a metadata in the file source provides information, minibpm is used to analyze and detect the file's BPM.
After tempo is estimated, the clip is time-stretched to match the session's tempo map. This means that should session's tempo change over time (in either ramped or constant mode), all audio clips will be re-stretched to accomodate for that.
Disabling stretching when original clip's tempo doesn't match that of the session will most of the times make the clip audibly go out of sync with the beat.
Once stretching is enabled, there are several options how to apply it:
This is where the estimated tempo is displayed. It can also be progressively divided or mutiplied by two.
Supposing, session's tempo is currently 120bpm and original clip's tempo is 90bpm. Stretching the clip to match session's tempo will make it sound faster that it originally is.
If the estimated clip's tempo is divided by 2, stretching the resulted 45bpm back to 120bpm will make the clip sound faster. Vice versa, multiplying the original clip's tempo by 2 and then stretching it down from 180bpm to 120bpm will make the clip sound slower than it originally is.
This control allows adjusting the estimated tempo in a finer manner, by changing the amount of beats it takes to play the clip in the selected trigger slot. The change is immediately displayed in the BPM field above.
This is an estimate of the clip's length as measured in bars for two popular time signatures: 4/4 and 3/4.