Ganeshji represents auspiciousness

Since Ganeshji represents auspiciousness, his whole being has symbolic imports for devotees.
Large ears signify listening to Gods katha with great zeal.
Small eyes to do the Lords darshan minutely.
Large forehead to develop great intellect to realise God.
Large stomach depicts his great capacity to empathise with the woes of devotees.
Short legs depicts patience.
Long trunk symbolic of his deep scriptural wisdom.
Mouse as vehicle a hyperactive creature, symbolic of our indriyas. Therefore Ganesh sitting on such a vehicle represents a deity of control over the indriyas.
Four arms which hold ankush symbol for control over the mind
ladu for happiness
pash axe to punish the indriyas and antahkaran
ashirvad mudra blessings for the well being of humanity
Depending on the role of Ganapati, the number of arms varies, as do the type of objects.