Origin and meaning
Gana (गण) + pati (पति)= Ganapati. Pati is the nurturer.
According to Maharshi Panini
Gana is a group of the eight vasus. The word vasu refers to direction or the guardian deity of the directions (dikpal or dikdev). Ganapati is the nurturer, master (swami) of the directions. (According to one school of thought, Ganapati is the master of the ten directions. The upward and downward directions along with the eight directions constitute the ten directions.) Other deities cannot reach the site of ritualistic worship (puja) from any direction without His permission. Hence any auspicious task or the ritualistic worship of any other deity is commenced with the ritualistic worship of Lord Ganapati. Once Ganapati clears the directions, the deity one is worshipping can manifest itself there. This itself is referred to as Mahadvarpujan or Mahaganapatipujan. [In the Ganpatya sect, the word Ganapati is used instead of Brahman (God) and Mahaganapati instead of Parabrahman (Supreme God).]
Lord Ganesha is the most widely worshipped Hindu God. He is worshipped at the start of any action or venture, for he is considered to be the Lord who removes obstacles (vignam) and hence is also called Vigneshwara.
He is considered a bachelor, but according to another school of thought, he has two Sakthis - Siddhi & Buddhi. Siddhi represents success and prosperity. Buddhi represents wisdom. His vahana is a tiny mouse (mooshikam or minjur).
One who eliminates distress caused by distressing energies
50% of good seekers are afflicted by distressing energies. An individual experiences physical or psychological distress due to distressing energies or he constantly encounters some or the other obstacle in his life. Distressing energies pose obstacles even in the spiritual practice of seekers and take the benefit of the spiritual practice of seekers. From this it is evident how necessary it is for everyone to give preference to overcome distress due to distressing energies. Information about how distress due to distressing energies like possession, black magic (karani), etc. can be overcome by repeating (chanting) the Name of Ganapati.
Sanatan Sanstha is an organisation undertaking the mission for the sake of society (samashti), that is propagating Righteousness (Dharma) in society. Just as Sanatan wants to 'reinstate the Divine kingdom', the distressing energies want to 'establish a demoniacal kingdom'. Hence presently distressing energies are posing obstacles in the spiritual practice undertaken by Sanatan's seekers as well as in the mission of propagating Righteousness, on a large scale. Sanatan's seekers undertake collective repetition (chanting) of 'Om Gang Ganapataye namaha' and 'Om namo Bhagavate Vasudevaya' aloud thrice each alternately as suggested by The Lord during meditation in order to alleviate this collective distress faster. They are also benefited by it. This illustrates that Ganapati has the potential to overcome the distress caused to society.
One who augments the vital energy (pranshakti)
Various body functions in man occur due to various types of energies. (Information about these various energies is given in 'Science of Spirituality : Chapter 35 - Pranayam'.) The basic energy of all these energies is the vital energy. Repetition (chanting) of the Name of Lord Ganapati augments the vital energy in our body.
Presiding deity of knowledge (Vidyapati)
There is an ancient custom of writing, 'Shri Ganeshaya namaha, Shri Sarasvatyai namaha, Shri Gurubhyo namaha', that is obeisance to Lord Ganesh, deity Sarasvati and the Guru, before beginning any writing, for example a letter. Why is this order followed? Knowledge of any subject is first acquired through the intellect and Ganapati is the bestower of intellect. Hence 'Shri Ganeshaya namaha' is written first. Deity Sarasvati's mission is to put into words the knowledge acquired through the intellect. Sarasvati is called "abhinav vagvilasini", the deity of development of speech by Saint Dnyaneshvar and "shabda mul vagdevata", the deity of the origin of words by Saint Samarth Ramdasswami. Hence, deity Sarasvati is second in the order. Since the Guru is the medium of acquisition of knowledge and its transcription into words, He is third in the order.'
The great epic Mahabharat
Maharshi Vyas wanted an intelligent writer to write the Mahabharat. So He prayed to Lord Ganapati to undertake this task.
Lord Ganesha Mantra.
This mantra, dedicated to Ganesh the beloved elephant-headed god of Hinduism, is chanted before any activity, ritual or puja is performed.
Mantra:
Vakratund Mahakaya Surya Koti Samaprabha
Nirvhignam Kurumedeya Sarva Karyashu Sarvada
Meaning: O Lord with the large body, curved trunk, and the brilliance of crore (10 million) suns, please free my work from all obstacles, forever.
Ganesha Gayatri mantram :
om tat purushaaya vidmahae
vakra dhundaaya dheemahi
tanno dhandhi: prachodayaat

Lord Ganesha Festival
4th day of Bhadrapad month in Hindu calendar is known as Ganesha Chaturthi. Though the vrat for lord Ganesha is observed on 4th day of Krishna Paksha of every Hindu month, but this is special of all. Ganesha Chaturthi or Ganesha Festival is a day on which Lord Ganesha, the son of Shiva and Parvati, is believed to bestow his presence on earth for all his devotees and hence celebrated as the birthday of Lord Ganesha. It is also known as Vinayaka Chaturthi or Vinayaka Chavithi. Siddhi Vinayak Vrat is also observed on this same day. While celebrated all over India, it is most elaborate in Maharashtra,Goa ( Biggest festival for Konkani people all over the world ) Gujarat, Karnataka and Andhra Pradesh, and other areas which were former states of the Maratha Empire. In this year 2008, this festival will be celebrated on 4th of September.
Om Gam Ganapathiye Namaha.......