MIDI Clock is a stream of messages sent by a MIDI sequencer of some kind that indicates musical tempo. It is used to maintain a synchronized tempo for synthesizers that have BPM-dependent voices and also for arpeggiator synchronization. It does not transmit any location information (bar number or time code) and so must be used in conjunction with a positional reference (such as timecode) for complete sync.
Ardour 2.X could pay attention to the start/stop/continue messages that are a part of the MIDI Clock protocol, but because it had no real notion of musical time in any particularly useful sense, no support for actually syncing to MIDI clock was provided.
Ardour 3.0 has full support for MIDI Clock sync, implemented by Hans Baier, and is capable of incredibly tight synchronization with the clock source. It will normally lock to the clock source within a few milliseconds and will remain in sync even if the clock source tempo is changed rapidly (e.g. by turning a tempo knob). You can select Clock Sync as the slave source from the Session -> Properties -> Sync tab, but note that as stated above, it does not provide a positional reference. However, when in this mode, Ardour will also pay attention to MIDI Song Position Pointer messages (SPP) so that locates and similar operations performed on the clock source will have an effect on Ardour’s transport position.