The oxidising property of nitric acid is based on the fact that when nitric acid undergoes decomposition, it yields nascent oxygen, which is very reactive.
2HNO3 (cone.) → H2O + 2NO2 + [O]
2HNO3 (dil.) → H2O + 2NO + 3[O]
This nascent oxygen oxidises metals, non-metals, organic and inorganic compounds. During the process, nitric acid itself gets reduced to various products (NO, NO2 , N2O, NH3 , etc.) depending upon the concentration of the acid, reaction temperature and activity of the metal with which it is reacting.