What Does Lord Ganesh Symbolize?

Lord Ganesh was responsible for synthesis of many ideologies,he is associated with prosperity but also is associated with knowledge.Like his wife Riddhi is associated with Goddess Lakshmi and wife Siddhi is associated with Goddess Saraswati.His huge stomach is symbol of a trader who usually has a wealthy lifestyle but also a symbol of a sage who has knowledge but leads a very sedentary lifestyle.
Lord Ganesha had many tools , out of which ankush (elephant goad) represents pushing and pulling of a elephant to control him.Parash also known as axe is symbol of analysis ,which means breaking down of ideas which is required while solving problems.Paash also known as rope is a symbol of synthesis ,which is to bring ideas together.Therefore he's responsible for both synthesis and analysis which leads to intellectually solving problems.

                              

Rat which is farmer's worst enemy is a symbol of problems and Lord Ganesh controls the rat , which is considered as controlling the problem.Also Lord Ganesha has a snake tied to his belly but the rat is not afraid that snake will attack him and even snake is content without attacking on the rat which is an impossible relationship between a prey and predator.This symbolizes harmony,contenment ,fearlessness and a secure environment.
Lord Ganesha's huge elephant head is sign of wisdom and power,his big ears and small mouth is a sign of listening more and speaking less which is important for being more wise, small eyes a symbol of concentration,his trunk can hold anything and everthing that exist in this universe which represent high efficiency and adaptability which helps in dealing with various situations that we go through over the course of life.