The word Namaste is formed by combining two word of Sanskrit “Namah”, followed by “Te”. Meaning of Namah– “Bow” and Te means “to you “.
it also has a spiritual representation of faith that the atman/Soul is same in me and you. So, Namaste means -it’s a salutation/bowing to that soul in you.
When after Yoga you say Namaste to others, it is also a transfer of the positive energy to others.It is also an expression of peace, gratitude, respect.
So, when in our daily life or in yoga we offer Namaste to someone, we are representing our faith that my inner soul greatly respects your soul, respecting the ultimate truth, light, peace and love with in you.