10. Symbolic Meaning of Ganesha

1. Elephantine Head - The big cranium of Ganesha cser thinking. It is equanimity
prudence.

2. Pepite Eyes - The small eyes indicate the focus is always needed in whatwe do. They are symbol of concentration. 

3. Large Ears - The large flappy ears tell us to be good listener. Thus large ears are a symbol of vigilant listening. 

4. Single Tusk - Ganesha has monosyllabic name AUM. Like his one sound name, the deity has one tusk. It a symbol of retention of good virtues. One should defy what is immoral.

5. Swirled Trunk - Ganesha's trunk is twisted left or right or protudes straight. It is a symbol of adaptability and dexterity. 

6. Rope or nook - The nook is symbol of Ganesha's support in tough times. The nook is an object of both offence and defence. It can be used for merit and support of good people or to anniliate evil forces.

7. Modaka - The Modaks are a symbolic assurance of rewards in return for good deeds, devotion and dedication.

8. Mouse - Mouse are attributed to hasty and impirsh. Similarly human mind tends to drift under the influence of various haoppenings. It is therefore mandatory to control the mind like mouse, else it would be clouded and void of focus. Thus the mouse is a symbol of enthusiastic control.

9. Axe - The axe held by Ganesha defies his ability to anniliate evil forces, and destroy all bonds of materialistic attachments.
10. Small mouth - The mouth of Ganesha lies under its trunk. It is small and reaffirms the need to talk less (and listen more with large ears).
 
11. Blessings - Ganesha reciprocates the devotional love of his devotees with blessings. The blessing hand is a symbolic assurance of is omnipresence and endurance towards his lovers.

12. Large belly - Ganesha is noted for his large protruding belly. The large belly has both material and physic significance. Materistically, or physically the large belly signifies abundance, prosperity and bountifulness. It also reaffirms Ganesha's large appetite. Cognitively the large abdomen relates to Ganesha's ability to assimilate both wise and wicked virtues. It is an indicative of his powers to anniliate the evil forces. (Read related story).
 
13. Prasada - The offerings made to Ganesha are accepted by him. It is a symbol of divine acceptance when he is served with tru devotion.

14. Firm Legs - The legs of Ganesha support his massive body. It conveys the message that we should stay afirm in times of trials. It tells us to keep faith and trust God. May be God tests us sometimes! 
Ganesha refers to the "lord of the hosts," (also spelled as Ganesa)

Other Common Names - Ganapati
One of the most well-known and venerated representations of Brahma.

Vinayaka in Marathi, Malayalam and Kannada
Vinayagar and Pillayar in Tamil
Vinayakudu in Telugu

'Ga' symbolizes Buddhi (intellect) and 'Na' symbolizes Vijnana (wisdom).
Thus considered the master of intellect and wisdom.

the position of his legs (one resting on the ground and one raised) indicate the importance of living and participating in the material world as well as in the spiritual world, the ability to live in the world without being of the world.
The four arms of Ganesha represent the four inner attributes of the subtle body, that is: mind (Manas), intellect (Buddhi), ego (Ahamkara), and conditioned conscience (Chitta). Lord Ganesha represents the pure consciousness - the Atman - which enables these four attributes to function in us;
The hand waving an axe, is a symbol of the retrenchment of all desires, bearers of pain and suffering. With this axe Ganesha can both strike and repel obstacles. The axe is also to prod man to the path of righteousness and truth;
The second hand holds a whip, symbol of the force that ties the devout person to the eternal beatitude of God. The whip conveys that worldly attachments and desires should be rid of;
The third hand, turned towards the devotee, is in a pose of blessing, refuge and protection (abhaya);
the fourth hand holds a lotus flower (padma), and it symbolizes the highest goal of human evolution, the sweetness of the realised inner self.
Ganesha is also defined as Omkara or Aumkara, that is "having the form of Om (or Aum) (see the section The names of Ganesha). In fact, the shape of his body is a copy of the outline of the Devanagari letter which indicates the celebrated Bija Mantra. For this reason, Ganesha is considered the bodily incarnation of the entire Cosmos, He who is at the base of all of the phenomenal world (Vishvadhara, Jagadoddhara). Moreover, in the Tamil language, the sacred syllable is indicated precisely by a character which recalls the shape of the elephant's head of Ganesha.
The broken tusk of Ganesha, as described above, stands primarily for his ability to overcome or "break through" the illusions of duality. However, there are many other meanings that have been associated with this symbol.
Ganesha and the Mouse
According to one interpretation, Ganesha's divine vehicle, the mouse or mooshikam represents wisdom, talent and intelligence. It symbolizes minute investigation of a cryptic subject. A mouse leads a clandestine life below the ground. Thus it is also a symbol of ignorance that is dominant in darkness and fears light and knowledge. As the vehicle of Lord Ganesha, a mouse teaches us to remain always on alert and illuminate our inner-self with the light of knowledge.
Both Ganesha and the Mooshak love modaka, a sweet dish which is traditionally offered to them both during worship ceremonies. The Mooshak is usually depicted as very small in relation to Ganesha, in contrast to the depictions of vehicles of other deities. However, it was once traditional in Maharashtrian art to depict Mooshak as a very large mouse, and for Ganesha to be mounted on him like a horse.Yet another interpretation says that the mouse (Mushika or Akhu) represents the ego, the mind with all of its desires, and the pride of the individual. Ganesha, riding atop the mouse, becomes the master (and not the slave) of these tendencies, indicating the power that the intellect and the discriminative faculties have over the mind. Moreover, the mouse (extremely voracious by nature) is often depicted next to a plate of sweets with his eyes turned toward Ganesha while he tightly holds on to a morsel of food between his paws, as if expecting an order from Ganesha. This represents the mind which has been completely subordinated to the superior faculty of the intellect, the mind under strict supervision, which fixes Ganesha and does not approach the food unless it has permission.