Ardour is a digital audio workstation, which mostly implies that it is a non-destructive, non-linear system. Edits in Ardour do not change any of the media data on disk (everything is done with meta-data). Ardour is designed to handle track counts that Audacity could not dream of (100+), does realtime FX processing (coming to Audacity in the next version) rather than having to process the data and write a new file on disk, and is generally much more capable for handling multi-track audio.
Each one has its place. If you are really just editing an audio file, Audacity is likely to have less of a learning curve. If you involved in music creation or composition or recording, Ardour is much more likely to be the appropriate tool.
I installed Ardour and spent a couple of hours trying to get Jack to work or something like that and gave up.