Namaste

We press our hands together and say this at the end of every practice.  
What are we saying?

Namah - sanskrit for "to bow", "to salute", "to adore"
-te - the prefix for "you" 

So literally "I bow to you" or "I salute you",
but also "I adore you" or "I respect you". 

The words are almost always accompanied by the gesture.  
Pressing the hands together in front of the heart is called
añjali mudrā or praṇāmāsana.  

Anjali  comes from anj-, which means "to honor".  Anjali then means "to give honor", or "salute in blessing/benediction"".
Mudra means "sign" or "seal". 

The two together then mean "salutation sign" or "sign of blessing".  

When the two hands connect at the heart's center, this blessing goes both directions.  Respect is given to the person being greeted - the two people come together in the same way that the hands come together. Respect is also being given to the person greeting - the divine and the practitioner come together and acknowledge that the same happens in the person being greeted. 

So the total meaning of "Namaste", pressing the hands together and bowing the head, can be best approximated with "I bow to the divine in you, and recognize the divine in me" and by that connection, realize that the divine within unites us all. 

Namaste.