Once, Gajamukhaasura a demon, with severe penance obtained invincible powers from Lord Shiva, with which he harassed all the gods who rushed to Ganesha for help. Ganesha while battling with Gajamukha realized he couldn’t be killed due to Shiva’s boon.
He cursed the asura to change into a mouse, got into it’s back and made the mouse his vehicle thereby keeping it the nastiness of the asura under his control.
Mooshak, the mouse signifies that mouse within each personality in the form of desires which can eat away even a mountain of merit! Ganesha riding on it teaches us how we can reach a state of not just controlling our many desires but also using them to spread goodness and serve the world.