Ganesha is Vighneshvara or Vighnaraja, the Lord of Obstacles, both of a material and spiritual order. He is popularly worshipped as a remover of obstacles, though traditionally he also places obstacles in the path of those who need to be checked. Paul Courtright says that "his task in the divine scheme of things, his dharma, is to place and remove obstacles. It is his particular territory, the reason for his creation."
Krishan notes that some of Ganesha's names reflect shadings of multiple roles that have evolved over time. Dhavalikar ascribes the quick ascension of Ganesha in the Hindu pantheon, and the emergence of the Ganapatyas, to this shift in emphasis from vighnakartā (obstacle-creator) to vighnahartā (obstacle-averter). However, both functions continue to be vital to his character, as Robert Brown explains, "even after the Purāṇic Gaṇeśa is well-defined, in art Gaṇeśa remained predominantly important for his dual role as creator and remover of obstacles, thus having both a negative and a positive aspect
Ganesha is considered to be the Lord of letters and learning. In Sanskrit, the word buddhi is a feminine noun that is variously translated as intelligence, wisdom, or intellect. The concept of buddhi is closely associated with the personality of Ganesha, especially in the Puranic period, when many stories stress his cleverness and love of intelligence. One of Ganesha's names in the Ganesha Purana and the Ganesha Sahasranama is Buddhipriya. This name also appears in a list of 21 names at the end of the Ganesha Sahasranama that Ganesha says are especially important. The word priya can mean "fond of", and in a marital context it can mean "lover" or "husband", so the name may mean either "Fond of Intelligence" or "Buddhi's Husband".
Ganesha is identified with the Hindu mantra Aum (ॐ, also called Om). The term oṃkārasvarūpa (Aum is his form), when identified with Ganesha, refers to the notion that he personifies the primal sound. The Ganapati Atharvashirsa attests to this association. Chinmayananda translates the relevant passage as follows:
(O Lord Ganapati!) You are (the Trinity) Brahma, Vishnu, and Mahesa. You are Indra. You are fire [Agni] and air [Vāyu]. You are the sun [Sūrya] and the moon [Chandrama]. You are Brahman. You are (the three worlds) Bhuloka [earth], Antariksha-loka [space], and Swargaloka [heaven]. You are Om. (That is to say, You are all this)
Some devotees see similarities between the shape of Ganesha's body in iconography and the shape of Aum in the Devanāgarī and Tamil scripts.