The symbolism of Ganesha is clear: a chubby god with an elephant's head who enjoys the beauty of life, who enjoys good clothes, who likes to eat good food, who always brings auspiciousness in life and who is a benevolent force that, when invoked, can help you to transcend your own shortcomings and limitations.
Mythologically, you can imagine Ganesha as a cosmic entity. Physically, you can experience him in your own body as the part of the body which takes you from primitive behaviour to rational behaviour, from instinctive behaviour to knowledgeable behaviour, from reactive behaviour to behaviour that is well thought out. In the psychic dimension, he is the guardian of all the shaktis, the powers, the feminine energies that are responsible for the creation and formation of life, of the body, of the mind, of sentiments and all other human experiences.
Ganesha is not the guardian of Parvati only. Parvati represents the Cosmic Shakti, and this Cosmic Shakti manifests in a myriad of forms; in the form of Lakshmi, Saraswati, Indrani or in any other form that you may like to conceive of it. The beauty of Ganesha is that he protects this Shakti and maintains the purity of Shakti, preventing it from being tainted by your ignorance.
Time, matter and memory are three important aspects. In your life, your memory is limited. You say that you have memory of this lifetime, but the memories that you hold of this life are not sharp and clear. You do not have the clear memory of what you did when you were young. Often people cannot even recall what they were doing on this day one year ago, or even remember what they did yesterday. Your memory is short-lived. Ganesha's capacity for remembering indicates that he has the memory of everything since the beginning of time until the present day. He is like the genetic imprint which contains all the information, right from day one of existence until today. He is the storehouse of knowledge, wisdom and information. Ganesha is the power; Ganesha is the shakti that bridges the gross and the physical with the spiritual and internal. It is a bridge between the two levels of experience, between the two dimensions: the gross and the physical, the psychic and the spiritual.
Another attribute of Ganesha is that he controls every kind of experience that enters the perception of consciousness; I am not using the term 'human perception', I am using the term 'perception of consciousness'. Perception of consciousness has to be understood in the right context. Right now you are aware, you are conscious, but you are not aware of each and every input of your senses. You are not aware of the functions and behaviour of your own mind, yet you consider yourself aware. Ganesha has homogeneous awareness, total awareness of the past and the present, and therefore he becomes the ruler, the controller of all experiences that occur in the realm of consciousness, and nothing is unknown to him.
Ganesha is also the controller of all the agents that give you either a positive or a negative understanding, knowledge or experience: the divine and the demonical, both. Ganesha controls the demonical and the detrimental forces through strategy, and guides the benevolent forces through logic and deep, internal, intuitive inspiration. After all, when you encounter bad people, when you are surrounded by bad people, what do you do to get yourself out of that situation? You too must be sharp, clear and careful to avoid situations that can be detrimental to you. You have to use strategies to manage the bad which has surrounded you, and that is what Ganesha uses when he has to control the negative hosts, the negative shaktis, the negative powers.
When Ganesha has to deal with the positive, uplifting powers and forces, he uses intuitive, logical awareness and inspiration. When the spiritual aspirant is lifted up from fear and confusion into conscious awareness, then right thought, right speech and right interaction become the trademark of human life. When the right action, right speech and right interaction become the trademark of human expression, then you can say, "Ganesha is my friend."