The fourth tithi (day four of the waxing or waning moon) in the Vedic calendar month of Bhadrapada, is the birthday of Ganesha. We honor Ganesha as the protector and remover of all obstacles honored during this time.
During the third lunar phase the mind manifests our desires into form. In the transition from the third to the fourth tithi, this form creates a protective quality within our minds. The deity connected to this tithi is Ganesha. This beloved Elephant God is the manifestation of a divine protective force.
Why is Ganesha connected to protection, and known as the remover of all obstacles? To understand this symbolism we can revisit the story of how Ganesha came to have his elephant head.
Lord Shiva was married to Parvati and he had to leave on long journey. Parvati became lonely while Shiva was away and so she decided to create their son, who is known as Ganesha.
Shiva finally returned home from his journey and much to his surprise there was a young boy outside the home. He was guarding the front door.Not recognizing Shiva he starting shouting to Shiva to go away. Ganesha held his position firmly as protector of his mother who was inside the house having her bath. Not knowing that Parvati had created their son Ganesha, Shiva was very angry with this boy and was outraged that he would not let him enter his own home. So he drew his sword and chopped off his head.
Parvati, hearing the noise outside, quickly ran out to where Shiva and Ganesha were and saw that Shiva had killed their son. She screamed at Shiva, asking him how he could have killed their son! At that point Shiva realized his grave error. So he told one of his soldiers to go into the forest and bring the head of the first living creature that they saw. It was an elephant, and they gave the elephants head to Ganesh and he sprung back to life.
Shiva and Ganesh developed a loving relationship based upon the respect that Shiva had for Ganesh and his fierce protection of his mother. It is this protective quality that is brought to our mind during the fourth tithi.
From the teachings of Aia Classes Guru,Souvik Dutta, we can even see the connection of Ganesha to the planets in Jyotish:
His elephant head is a symbol for Wisdom in the Vedic tradition and this connects to the planet Jupiter. Shiva, who is Ganesha's father is the atma-swarupa (our true nature), or our soul which is shown by the Sun (Surya) in the horoscope. When Ganesha is headless, before Shiva's soldiers found the elephant head can be connected to the headless planet Ketu.
On Ganessha Chatirthi there are a number of ways to honor Ganesha. You can fast from sunrise to sunset. Or create a Ganesha yantra! I did this yantra practice for one full year on the fourth day of the waxing lunar phase. It is a powerful practice for removal of obstacles.
You can chant a mantra for Ganesh:
Lapitthya Jamboo Phalcharu Bhakshanam
Namami Vighneshwar Padpankajam
Translation: (I Salute) Sri Gajananam ( Who is having an Elephant Face ), Who is Served by the Bhuta Ganas (Celestial Attendants or Followers) and Others. Who Eats the Core of Kapittha (Wood Apple) and Jambu (Rose Apple) Fruits. Who is the Son of Devi Uma (Devi Parvati) and the Cause of Destruction of Sorrows. I Prostrate at the Lotus-Feet of Vigneshwara ( the God Who Removes Obstacles )
vakratunda mahaakaaya suryakoti samaprabhaa nirvighnam kurumedeva sarvakaaryeshu sarvadaa
Translation: Salutations to the supreme Lord Ganesh, whose curved trunk (vakra-tunda) and massive body (maha-kaayaa) shines like a million suns (surya-koti) and showers His blessings on everyone (sama-prabhaa). Oh my lord of lords Ganesh (kurume-deva), kindly remove all obstacles (nir-vighnam), always (sarva-) and forever (saravada) from all my activities and endeavors (sarva-kaaryeshu).