Gayatri Mantra

OM BHURBHUVAHA SWAHA TATA SAVITUR VARENYAM

BHARGODEVASYA DHIMAHI DHIYO YO NAHA PRACHODYAT

Om has three Hindi words. Aa, Uu and Ma.

Aa is meant for Aakaar from which three names of God are built, Viraat, Agni, and Vishwadi

Uu = uukar from which Hirannyagarbha, Vayu and Tejas names occur and

Ma = makaar from which Ishwar, Aditya and Praajyan aadi, holy names of God occur.

Rigveda mantra 1/164/46 says God is one but His names are several. But here OM the holy name of God is only being explained.

VIRAAT = Viraat word is made from dhatu 'Rajrideeptau' i.e., manifest. Therefore Viraat means He who manifests the universe. As God manifests the universe, thus Viraat is the name of God. Rigveda mandal 10, sukta 129 states that like potter makes pot from clay, similarly God creates universe from non-alive matter prakriti. Prakriti is unseen matter. From unseen matter, the whole universe is created in the visible form. Science also says that matter is never destroyed but changes its form. Suppose a paper is burnt, paper changes its form into ashes. Then ashes are crushed and thrown in air. At this moment, the paper changed into ashes becomes invisible but was never destroyed. Similarly the whole universe at the time of final destruction is turned into prakriti i.e., into unseen form.

AGNI = From dhatu, "ANCHU GATI POOJANAYOHO" the word "AGNI is made. Its meaning is: He who is a form of wisdom. "SARVAJAYEN" i.e. Omniscient. That is, knows each and every atom of universe and even beyond universe. He who is to be known, to be gained and is worshipful. So Agni is the name of God.

VISHWA = Vishwa word is made from dhatu, "VISHPRAVESHANE". Its meaning is He in whom the universe is entering or He who is entering the universe. So being omnipresent, Vishwa is the name of God.

HIRANNYAGARBHA = i.e., " JYOTIRVAYIHIRANYAM". Its meaning is, who is the base of all sun, etc., luminous lokas or He who is the living place of all luminous lokas. 

VAYU = from dhatu, "VA GATIGANDHANYOHO", vayu word is made. Its meaning is He who holds, gives life and destroys and is the mightiest amongst all. So the name of God is Vayu. 

TEJ = from dhatu, "TIJA NISHANE", the word Tej is made meaning He who is self made and self-enlightened and gives light to sun, moon, stars etc. God does not take light from anywhere but gives light to sun, moon, stars, etc. so the unbroken, unobstructed/unproduced and eternal form of light is Almighty God and not sun, moon etc. So the name of God is Tej.

ISHWAR = from dhatu, "ISH ASHWERIYE", the word Ishwar is made. Its meaning is whose knowledge is thoughtful and true and He who has unlimited wealth, fortune and glory etc. Therefore the name of God is Ishwar. Here it is not out of place to mention that soul (man/woman) has limited qualities and are dependent whereas God is independent and has unlimited qualities that is why He is God.

ADITYA = from dhatu, "DO AVAKHANDANE", Aditya word is made. Its meaning is the one who cannot be broken into pieces and thus cannot be destroyed. So God's name is Aditya.

PRAJAYEN (PRAGYA) = from dhatu, "JYEN AVABODHANE", Prajayen word is made meaning whose wisdom is totally without any misunderstanding and thus he who knows every matter and behavior of whole universe without misunderstanding. So God's name is Prajayen. So here also it is not out of place to mention that illusion can never attack on God and God is totally free from illusion.

BHUHU = "BHUHU ITI VAYEE PRANAHA" i.e., He who is the base of lives of universe, is most beloved, even more than Prann i.e., breath. So Bhuhu is the name of God. 

BHUVAHA= "BHUVAHA ITI APANAHA" i.e., He who is totally free from any sorrow, and the soul removes his own all sorrows after coming in contact with Him. So the name of God is Bhuvaha.

SWAHA = i.e., "SWAHA ITI VYANAHE" who is omnipresent in the universe and is holding the same. So the name of God is Swaha.

SAVITUHU = He who creates the universe. So the name of God is Savituhu. 

DEVSYA= who gives all pleasure/merriment, so the name of God is Dev. 

VARENNYAM = He who is the most supreme and acceptable. God is most supreme and acceptable for worship. 

BHARGAHA = the purest entity (though God is formless, but finding no suitable English word of Sanskrit word, "SHUDH SWARUPAM" the word entity has been used.) 

TAT = i.e., the God i.e., of the purest entity. 

DHIMAHI = i.e., we must hold (sort of meditation) because 

YAHA = the God

NAHA = our,

DHIYAHA = mind(i.e., in our minds) 

PRACHODYAT = by inspiration (fulfil the mind with wisdom) 

MEANING 
"We meditate the God who is the base of lives' of universe, totally free from any sorrow, omnipresent, creates the universe, gives all pleasure/merriment, most supreme and acceptable, purest entity; May the God enlighten our minds with wisdom by His inspiration". 

Here it is not out of place to mention that idea of a (one) Ved mantra is based on ideas of several Ved mantras.

So in the above Gayatri mantra, there are three things:

Bhuhu, Bhuvaha, Swaha, Savituhu, Bhargaha, Devsya are some qualities amongst unlimited qualities of God. These are called Stuti i.e., to say about God with His real qualities and not self made etc.

Dhimahi means meditation i.e., one should always sit in meditation and do hard and pious deeds for which he will have to study Vedas in full, while discharging moral duties towards family and nation. 

Dhiyo Yo Naha Prachodyat. It is a prayer to God explanation of which is cited above.