Below is an extract from the Skanda Purana Chapter 9, verses 34-50 which explains the significance of Arunachala girivalam.
If anyone regularly circumambulates the Lord in the form of Sonacala, he has no rebirth. He shall certainly attain eternity.
If a person takes even a step by way of circumambulation, the entire earth is sanctified by coming into contact with the dust of his feet.
With palms joined in reverence he should make obeisance in every direction. He should then meditate and eulogize. He should circumambulate slowly without his hand touching anyone else.
Without any agitation, without even hearing the sound of his own steps, the devotee should circumambulate in the manner of a woman walks when delivery is imminent.
The learned devotee should put on a clean dress after bath. He should apply sacred ash over his body and adorn himself with rudraksa beads. Remembering Siva he should take steps slowly.
He should think about the likelihood of collision with thousands of Devas, invisible Siddhas and others of gaseous forms. He should be a true devotee and go ahead slowly putting down his steps along the path.
Or the devotee should circumambulate along with other devotees chanting the names of Siva, singing excellent songs and dancing like Siva.
Or he should, with his mind not dwelling on anything else, listen respectfully to my greatness and circumambulate slowly feeling the thrill of the bliss.
He must offer different kinds of charitable gifts. He must perform meritorious deeds. He should render assistance to supplicants. He should be pious and merciful in a manner he thinks best. Thus he should move around.
In Krtayuga the Linga is fiery. In Treta it is a jewel mountain. In Dwapara one should think about it as golden and in Kaliyuga it is an emerald mountain.
Or he can meditate upon the red crystalline form that is self-luminous. Meditating thus, he will be freed from all sins. He shall go to the city of Siva.
This Linga with the name of Arunachala is the greatest on account of its inscrutability resulting from its state of not being an object of speech and mind and also because of its fiery nature. It is unapproachable. But I become approachable immediately to the person who circumambulates after meditation.