Tranquillity is a sense of peace and quiet. It is the feeling you have while sitting under a starry sky, listening to the crickets. The aura of tranquility comes from the calm in the world, which makes you feel you are without a care in the world.
Tranquillity is also sometimes spelled with one l as tranquility. Its roots are in the Latin trans meaning "exceedingly" and quies meaning "rest" or "quiet." Tranquil means calm, and something that is exceedingly quiet or restful — a sunset or a rocking chair in the shade — can give you a sense of tranquillity or peacefulness.