The gesture Namaste represents the belief that there is a Divine spark within each of us that is located in the heart chakra. The gesture is an acknowledgment of the soul in one by the soul in another. "Nama" means bow, "as" means I, and "te" means you. Therefore, Namaste literally means "bow me you" or "I bow to you."
To perform Namaste, we place the hands together at the heart charka, close the eyes, and bow the head. It can also be done by placing the hands together in front of the third eye, bowing the head, and then bringing the hands down to the heart. This is an especially deep form of respect. Although in the West the word "Namaste" is usually spoken in conjunction with the gesture, in India, it is understood that the gesture itself signifies Namaste, and therefore, it is unnecessary to say the word while bowing.
We bring the hands together at the heart chakra to increase the flow of Divine love. Bowing the head and closing the eyes helps the mind surrender to the Divine in the heart. One can do Namaste to oneself as a meditation technique to go deeper inside the heart chakra; when done with someone else, it is also a beautiful, albeit quick, meditation.
For a teacher and student, Namaste allows two individuals to come together energetically to a place of connection and timelessness, free from the bonds of ego-connection. If it is done with deep feeling in the heart and with the mind surrendered, a deep union of spirits can blossom.
Ideally, Namaste should be done both at the beginning and at the end of class. Usually, it is done at the end of class because the mind is less active and the energy in the room is more peaceful. The teacher initiates Namaste as a symbol of gratitude and respect toward her students and her own teachers and in return invites the students to connect with their lineage, thereby allowing the truth to flow—the truth that we are all one when we live from the heart.
I found a few different translations or definitions of Namaste, but the one I like most is this:
I honor the place in you in which the entire universe dwells. I honor the place in you which is of love, light, peace and joy. When you are in that place in you and I am in that place in me, We Are One.