Fox hunting, duh. Heck, why the heck do you think the Post Horn Gallop is played before every game?
Before you ask; yes, it is very strange that we're named after the prey of the very thing that was targeted in the hunts, but hey, Foxes are a big thing in Leicester, just look at the city coat of arms.
Fun Fact: We became Leicester City in 1920, shortly after Leicester itself was given back its City status.
The flower is the cinquefoil, which is one of the oldest floral symbols in British history (11th century), older than the darn roses! It was the symbol of Leicester's first Duke, Robert Deaumont.
Also, did I ever mention that there are still places, even notable ones, that use the wrong crest? Hint: The fox has white fur, a feature that came with our 125th anniversary. The older one has the same colour throughout the fox's face.