According to hindu mythology, the Lord Ganesha is shown sitting on ‘a mouse’, extending the symbolism, Lord Ganesha is associated with ‘knowledge’ & mouse with ‘reasoning’, the base over which the knowledge exists. In a simpler words , it is basically the extension of epistemology & its deep underlying principles, which defines the knowledge as an intersection between beliefs & truth.
The shloka is basically a manifestation of Shree Ganesha, he is the hindu deity whose blessings are seeked by all & sundry before every task. It translates as
O mighty God with a big belly and with the radiance of thousand suns
Always bless me to complete my every task by removing obstacles.