Nitric and hydrochloric acids act in synergy to make the mixture more effective. Nitric acid alone can dissolve some metals (e.g. copper) because it is a fairly strong oxidizing agent. However, it is not strong enough to oxidize very noble metals like gold or platinum. HCl brings chloride ions, which form effective complex ions with metals like Au and Pt. So, aqua regia provides both oxidation and complex ion formation which together combine to be enough of a push to get gold to dissolve.
That hydrochloric acid is an acid is almost just a footnote. HCl isn't any better than HNO3 at providing H+ (both are "strong" acids). The acidity does help keep the oxidizing strength of nitrate high, but the chloride is the more important part. For example, a mixture of nitric and sulfuric acids would not have the same value as nitric + HCl.