I have been chanting that mantra every morning to today and don't have a clue of what it means.
But I realize that the sound produced while chanting that mantra is the most important part; I still want to know its meaning.
Gayatri is Rig veda (III. lxii. 10.) Ralph Griffith's translation is
May we attain that excellent glory of Savitar the God :
So May he stimulate our prayers.
A better translation might be :
We meditate on the glory of that Being who has produced this universe.
May He enlighten our minds
The mantra meaning:
"O thou existence Absolute, Creator of the three dimensions, we contemplate upon thy divine light. May He stimulate our intellect and bestow upon us true knowledge."
"O Divine mother, our hearts are filled with darkness. Please make this darkness distant from us and promote illumination within us."
The word "Gayatri" itself explains the reason for the existence of this mantra. It has its origin in the Sanskrit phrase Gayantam Triyate iti, and refers to that mantra which rescues the chanter from all adverse situations that may lead to mortality.
Goddess Gayatri is also called "Veda-Mata" or the Mother of the Vedas - Rig, Yajur, Saam and Atharva - because it is the very basis of the Vedas. It is the basis, the reality behind the experienced and the cognized universe.
Bhuh Bhuvah Svah
Tat Savitur Varenyam
Bhargo Devasya Dheemahi
Dhiyo Yo nah Prachodayat