Physiologically:
The left lung is smaller than the right lung because the heart is left of center in the body. The liver is on the right side and is the largest, heaviest internal organ, with an average weight of 3.5 pounds. When you roll to your right side, the heart remains open and free of pressure. The heart also remains above the organs leaving less weight on the heart resulting in less pressure after Savasana. Interestingly, in some people the internal anatomy is reversed, with hearts on the right and/or livers on the left, but are otherwise perfectly healthy. In this case the student would benefit from rolling onto their left side.

When pregnant, it is best to roll onto the left side. Rolling to the left side improves circulation, giving nutrient-packed blood an easier route from the heart to the placenta nourishing the baby. Lying on the left side also relieves the pressure of the uterus from lying on top of the liver, which is essential in the processing of nutrients and detoxification of non-nutrients.

Philosophically:
In India, it is considered auspicious to enter a holy space with your right foot. In many parts of the world we greet each other by extending our right hands. The right side represents the east and rolling towards the east, or the rising sun, is symbolic of asking for blessings of grace and bliss.

Energetically:
In traditional Indian and Chinese medicine, our body contains over 72.000 nadis, or energy channels. There are three “main” nadis in the body: the Sushumna in the center of the spine, the Ida nadi on the left side, and the Pingala nadi on the right side.

The Ida and the Pingala nadis are associated with specific attributes. The left side of the body, or the Ida nadi, is related to our femininity. The feminine side of the body has cooling, calming, Yin energy. The right side of the body, or the Pingala nadi, is related to our masculinity. The masculine side of the body has heating, energizing, Yang energy.

When you come out of Savasana and roll to your right side, your left nostril is on top. This will emphasize the flow of breath through the left nostril, and has a calming effect. Since we generally want to calm the body and the mind when we practice yoga, we end the class in this position. If you need some stimulation and extra energy at the end of your practice, it is advised to roll to your left side to stimulate breathing through your right nostril.

References: https://www.webmd.com/baby/positioning-while-sleeping, http://www.sciencefocus.com/qa/top-10-what-are-heaviest-organs-human-body, http://www.healthandyoga.com/html/dissertations/shruddha1/abstract.aspx, https://www.melissawest.com/why-we-roll-to-the-right-side/, https://www.quora.com/Is-it-true-that-we-have-the-right-side-bigger-than-the-left-or-opposite-Why