Apparently hugging triggers the release of oxytocin in the brain. The effects are both immediate and residual. Studies have shown that hugging reduces the chance of illness, lowers blood pressure and minimizes the effects of depression and grief.
The benefits of human hugging are apt metaphors for what God's embrace of us accomplishes in the person of Jesus. Think of the old hymns like "Blessed assurance, Jesus is mine" or "I come to the garden, alone." Disregarding the overly individualistic language, what happens in both songs is a description of blessing that comes through one's proximity to the person of Jesus. Good feelings, release from torment or pain, simply are the effects of being embraced.
The meaning of this for us is that embraces -- both the ones we extend to each other and especially the one that God offers -- are confirmed by real experience. In the case of our experiences with each other the research is fairly conclusive. In the case of God's embrace of us it is known most assuredly in the life, death and resurrection of Jesus of Nazareth. That is to say it is incarnated by all that Jesus does and all that God does through him.
Nothing demonstrates God's embrace of humanity more than the realities of the incarnation, its fulfillment and most completely in God's raising Jesus from the dead. Altogether it says "I am with you," "be not afraid," "trust me," "stay close." Like one cosmic and eternal hug from God.
There is much for us to learn from this gift of divine embrace and there is just as much for us to do in response. Perhaps most important is that we hug God back; especially in less than ideal moments and in ways particularly meant to help others recalibrate their embracing.
One caveat: hugging people for no reason may not be the best demonstration of God's embrace. Duh! It's just like being overly focused on a bread recipe that will not accomplish all that we hope in making eucharist. That is to say outward and visible signs beg an inward and spiritual grace, an intention, a purpose, a commitment to be real after the hug and beyond the ceremony.