tat saviturvarENyaM bhargO dEvasya dhimahi

Upanayanam is a ceremony that initiates a devout Hindu to a life of celibacy and devoted education. During this important ritual that helps in leading a pious life, it is the role of the father, guardian or a guru to whisper a sacred mantra into the ears of the child being initiated. The process involves spreading a cloth around the heads and shoulders of both the parent and child so that no one can neither see nor hear the sacred knowledge that is being transferred. Starting from that initiation point, the student becomes worthy of studying vedas and chanting the most sacred of all Hindu verses called Gayathri mantra. It is said ‘Gayantham Trayate ithi Gayatri’ meaning Gayathri mantra protects the one who recites it. Let’s take a look at this sacred mantra, its source and its significance.

OM bhur bhuva suvaH tat saviturvarENyaM bhargO dEvasya dhImahi dhiyO yona pracOdayAt We meditate upon the Spiritual Effulgence of that Adorable Supreme Divine Reality, the Source of the Physical, the Astral and the Heavenly Spheres of Existence. May that Supreme Divine Being enlighten our intellect.

Meaning
The meaning of this mantra, varies depending on who is interpreting. Brahmo Samaj and Arya Samaj have their own interpretations that are very different from each other. The different meanings arise from the interpretation of the words bhur, bhuva and suvaH. One reference is to the three worlds: bhur(earth), bhuva(astral) and suvah(heaven). The other reference is to the three attributes: bhur(embodiment of vital energy), bhuva(destroyer of sufferings) and suvah(symbol of bliss). SuvaH is often pronounced as svaaH. SvaaH is another word for svarga or suvarloka. The essence of this mantra is to seek guidance of that power, which created the three worlds or the power that possesses the three attributes, to inspire righteous intellect in the seeker.

One often hears the long form of this mantra especially at rituals:

OM bhur OM bhuvaH OM suvaH OM maH OM janaH OM tapaH OM sat yaM
OM tat savitur vareNyaM bhargo devasya dhImahi dhiyo yo naH prachodayAt

It is difficult to ascertain in simple words and in a logical way as to why this mantra is called Gayatri mantra. Without being overly indulgent here is my attempt: Goddess Gayatri is considered to be the face of the Vedas and an embodiment of all gods and all mantras. This mantra is the basis of all Vedas. Hence this may be referred to as Gayatri Mantra.

Source
10th mantra of 62nd hymn of Rig Veda’s 3rd mandala, referred to as Rig Veda 3.62.10, is the source of this mantra. Brahmarshi Viswamitra is credited as the author of the 3rd mandala of Rig Veda including the Gayatri Mantra. Ralph T.H. Griffith(1826-1906), a British indologist who served as the principal at the Benares College, provided an English translation of the Rig Veda. This translation is considered an authority in the western world and is published on sacred-texts.com. This mantra in its original form is as follows:

tat saviturvareNyaM bhargho dEvasya dhImahi |
dhiyo yo naH pracodayAt ||

The words OM bhur bhuva suvaH constitute a mandatory prefix called mahAvyAhruti or great utterance.

Significance
According to the puranas, sage Viswamitra is considered to be the first one to fully understand and therefore wield all the power of Gayatri mantra. Among 24 such rishis Yagnavalkya is considered to be the last one to realize the potent power of Gayatri Mantra.

Of all the sacred mantras, Gayatri mantra is perhaps the most commented upon mantra. One finds several references to the significance and power of this mantra across the entire breadth of Hindu mythology and its sacred texts. In addition there are several books and commentaries written by great saints and contemporary spiritual leaders. I pick just two of my favorites:

• Bhagavad Gita: In chapter 10 verse 35, while referring to the best of all the attributes among all creation, Sri Krishna declares that He is the Gayatri among the poetic meters(of 24 syllables) alluding to the power of Gayatri mantra which is its chief hymn.
• Manu: In Manu Smriti, there are several verses on the significance of Gayatri mantra and its recitation methods. In the 83rd verse of chapter 2 , Manu declares that there is no mantra that is more powerful than the Gayatri mantra.

During the thread ceremony or upanayana one gets initiated into the Gayatri mantra. From that point onwards this mantra is recited every day before partaking meals as well as during the daily prayers called Sandhya Vandanam.

Any Hindu ritual is incomplete without reciting this mantra at least once during the process.

The Gayatri has three parts – Praise,  Meditation, and Prayer. First, the Divine is praised, then it is meditated upon in reverence and lastly, an appeal is made to the Divine to dispel the darkness of ignorance and to awaken and strengthen the intellect. “Dheemahi” is related to the meditative aspect. “Dhiyo Yo Nah Prachodayat” relates to the aspect of prayer. Chanting of the Gayatri Mantra purifies the mind and confers devotion, detachment and wisdom. Chanting of the Gayatri Mantra will sanctify man’s life.

– Excerpt from a speech delivered by Bhagavan Sri Sathya Sai Baba on Feb 10, 2000

Additional Reference:
http://en.wikipedia.org/wiki/Gayatri_Mantra