What Is The Origin Of The Phrase "To Sow One's Wild Oats"?

Wild oats are actually the Avena fatua plant.  This is a common wild weed in Europe.  It resembles domesticated oats (the ones we grow, harvest and eat).  It is difficult to eradicate and spreads quickly in agricultural fields, hence it's reputation as a pernicious organism.

Sowing Avena fatua could therefore mean to cast about wildly to see what develops.

Avena fatua also has a reputation as a traditional herbal remedy, specifically to increase one's sex drive.  So sowing one's "wild oats" obviously has quite a different meaning in that context, mostly related to the strong impulses (including sexual) of youth.  Just having the reputation as a strong aphrodesiac may be where the saying came from.  It is believed to date back to at least Roman times.

There is no decent quality evidence to verify that extracts of Avena fatua are actually any good at increasing one's sex drive.