What is the significance of Gayathri Mantra? On what occasions is this Mantra used? Also, what is the meaning of the Gayathri Mantra? Will be grateful for an explanation.
A typical gāyatrī mantra indicates three things: situation, process and goal. There are many gāyatrī mantras, e.g.:
In all cases the Deity is typically addressed as all three — the surrounding, the uplifter and the ultimate goal. As the result of chanting, you will reach the Deity (mantra siddhi) and receive His blessings. Gāyatrī mantras are supposed to be somewhat secret, so I will not delve on their content in detail. They should be received from an empowered Guru who can ensure your success in chanting.
Gāyatrī is also a meter of 3 padas (quarters) of 8 syllables each. It is the shortest of all meters (24 syllables), followed by anuštubh (32 syllables), brihati (36 syllables) and others. Being the first of all meters, Krišna claims to be gāyatrī (Bhagavad-gītā 10.35: gāyatrī chandasām aham).
AUM, the Supreme name of God. A full explanation of this has been given in a related article.
BHUR BHUVAH SWAH. These three words collectively are known as the "Mahavyahriti". They express the nature of God, and demonstrate his inherent qualities.
TAT. Literally, this word means "that", being used in Sanskrit to denote the third person. It is also mentioned in the Bhagavad Gita by Sri Krishna Himself, where He implies the selfless nature of the word.
SA-VI-TUR. Savita, from which Savitur is derived, is another name of God, this being the reason that the Gayatri Mantra is often known as the Savitri Mantra.
VA-RE-NY-AM. Varenyam signifies our acceptance of God, and can be translated as meaning "Who is worthy".
BHAR-GO. Bhargo is taken to signify the Glorious Light that is God's love and power.
DE-VAS-YA. The word Deva, from which this word is derived, has been translated by different people in many different ways.
DHI-MA-HI. Meaning to meditate and focus our mind on God.
DHI-YO. Sanskrit for "intellect", this is the essence of this part of the Gayatri Mantra.
YO. Meaning "Who" or "That", Yo signifies yet again that it is not to anyone else that we direct these prayers, but to God alone.
NAH. Nah means "Ours", and signifies the selflessness of the request we make of God in this part of the Gayatri Mantra.
PRA-CHO-DA-YAT. Prachodayat, the final word of the Gayatri Mantra, rounds off the whole mantra, and completes the request we make of God in this final part.