Ādi- is a common prefix in the Sanskrit language, denoting "in the beginning", "the first" or "the original". Śeṣa means "residue", "remainder", the leftovers. Śeṣa is also one of many words that is used to mean "snake", in this case referring to the snake's characteristic quality of shedding its skin. It slithers away, "reborn" as something new, but it leaves behind the cast-off skin, its residue. Hence, Adishesha can be understand as "the primordial snake". This metaphor is the basis of a common theme in yoga philosophy; the idea that all of our actions whether mental or physical, are intrinsically imperfect and incomplete due to our impermanent nature. Our actions therefore leave a residue, creating karma which then becomes the basis of necessary future action.
In Hindu mythology Adishesha, sometimes also known as "Ananta" (The Endless One), is the thousand-headed ruler of the Nagas, the serpent race that is thought to guard the hidden treasures of the earth. Since yogic knowledge is the ultimate the secret treasure, many yogins still bow to Adishesha before beginning their daily yoga practice. "Salutation to the king of the Nagas, to the infinite, to the bearer of the mandala, who spreads out this universe with thousands of hooded heads, set with blazing, effulgent jewels."
Hindu iconography often depicts Adishesha as floating on the ocean, his long snake body coiled to form an expansive comfortable couch on which the god Vishnu rests with lakshmi and reclines during the intervals of creation. The serpent's thousand heads symbolize infinity or omnipresence. These heads reach up and out like a protective canopy or umbrella over Vishnu and on that "umbrella" rests our earth.
The snake's body is soft and gentle enough to serve as a couch for a god and at the same time, firm and steady enough to support the whole earth. We endeavor to bring both of these same qualities to our asana practice : softness, comfort and ease(sukha) must be balanced with firmness, strength and steadiness of effort (sthira). As Patanjali succinctly put it in the Yoga Sutra:
sthirasukhamāsanam (YS 2.46) (source:adishesha.com)