There is a relation between the feminine and big cats. Carl Jung notices the link when he said that the anima “can appear as a … tiger” (CW 9i, para. 358). In dreams, imagination, art we may find powerful female figures appearing as or with a big cat such as cougars, pumas, mountain lions, panthers, leopards, jaguars, etc. It seems rather likley that the big cats represent feminine power. To confirm this intuition we may turn to the above image of the Hindu Goddess Durga. She appears with her lion.
In the image, we see the lion is killing the demon Mahishasura. Mahishasura is part asura (demon) and part Mahisha (buffalo). Mahishasura wanted to kill off the deities, but the Durga and the lion fight the demons and win.
Reference: Carl G.Jung, The Archetypes and the Collective Unconscious – Collected Works volume 9i (originally published 1934–1954)