Audio tracks in Ardour have a mode which affects how they behave when recording:

Normal Tracks in normal mode will record non-destructively—new data is written to new files, and when overdubbing, new regions will be layered on top of existing ones. This is the recommended mode for most workflows.
Non-Layered Tracks using non-layered mode will record non-destructively—new data is written to new files, but when overdubbing, the existing regions are trimmed so that there are no overlaps. This does not affect the previously recorded audio data, and trimmed regions can be expanded again at will. Non-layered mode can be very useful for spoken word material, especially in combination with push/pull trimming.
Tape Tape-mode tracks do destructive recording: all data is recorded to a single file and if a section of existing data is overdub, the existing data is destroyed irrevocably—there is no undo. Fixed crossfades are added at every punch in and out point. This mode can be useful for certain kinds of re-recording workflows, but is not suggested for normal use.
Normal and non-layered overdubbing comparision
Normal and non-layered overdubbing comparision

The screenshot on the right shows the subtle difference between an overdub in normal mode (upper track) and one in non-layered mode (lower track). Both tracks were created using identical audio data.

The upper track shows a new region which has been layered on top of the the existing (longer) region. It can be seen by the region name strips.

The lower track has split the existing region in two, trimmed each new region to create space for the new overdub, and inserted the overdub region in between.