Everybody, whether he/she believes in god or not, leaves for happiness and freedom. Is there anyone who does not like to be happy? All our activities likes building bank balance, and investments in mutual funds or property, etc are because we do not want to be in trouble. Trouble induces sadness. So dukha-nrivritti is nothing but sukha. This samsara goes on in a quest to be happy. If given freedom, one will always choose work or object which one likes (i.e. makes one happy).
Nature of Atman is Sat-Chit-Ananda.
Out of this, ananda (happiness) is easily experienced by us in practical life. But this ananda has 'vikara' i.e. it depends upon external person or object which is not permanent.
On Surrendering to God, one's attachment with worldly objects decreases, ego begins to melt. This makes one's mind light and one begins to experience divine love. This love is long lasting, since it does not depend upon anything else, unlike general happiness which is temporary. Detachment from 5 senses and it's objects instantly induces peace and bliss. This is vairagya - absence of 'bhogya padartha'.
E.g. you enjoy ice-cream, but that enjoyment exist only till you eat ice-cream.
When both happiness and God's love are compared, one finds that God's love is more deep and long lasting.
While meditating on God or Brahman or Atman, one experiences that he/she is different from thoughts and 5 senses which constantly pull him in extrovert direction. He/she begins to dis-identify from them. This dis-identification brings one peace.
In the case of bhakta, he compares everything with God and gives more important to God's holy name, thus unknowingly detaching himself from sense objects and thoughts.
Mind becomes calm and filled with peace and love. This triggers brain to release harmones which induce peace and calmness. Body rejuvenates, and self healing is accelerated. Diseases of emotional origin begin to cure and one have less chance of them developing them. Since brain refreshes, psycho-somatic diseases also does not happen. Digestion increases and one becomes balanced, emotionally and physically.
In today's age of anxiety, stress, tension and excessive competition, it is extremely necessary to live a Spiritual Life (of Prayer, Surrender and Meditation) - Read this
Some scientific explanation.
Brain waves, which in day time are vibrating in beta frequency (concrete thinking), now shifts to alpha, in which both left and right hemispheres are active, then goes to thetha, where one experiences deep spiritual connection, then to delta, in which one becomes un-aware of his body, similar to deep sleep, but is conscious.