In Sanskrit the word is namah + te = namaste which literally means “I bow to you” - my greetings, salutations or prostration to you. The word ‘namaha’ can also be literally interpreted as "na ma" (not mine). It has a spiritual significance of negating or reducing one's ego in the presence of another.
The reason why namaste has a deeper spiritual significance is that it recognizes the belief that the life force, the divinity, the Self or the God in me is the same in all beings. Acknowledging this oneness with the meeting of the palms, we honor the god in all people we meet.