Garuda is the King of Birds. He’s the protector and personification of courage. He has the power to swiftly go anywhere. Garuda is the vahana [vehicle mount] of Vishnu. Garuda‘s wings are powerful enough to stop the spinning of the 3 worlds and vast enough to block the sun.
Garuda is the younger brother of Aruna [Charioteer of the sun god, Surya]. Aruna and Garuda were born to Vinata, mother of birds. Vinata and Kadru, wives of Kashyapa, each wanted to give birth to powerful children. Kadru, mother of nagas, [serpents] gave birth to 1,000 snakes. Vinata gave birth to just Aruna and Garuda, but asked that they be more powerful than all of Kadru‘s children. Vinata was impatient with Aruna’s hatching and realved him too soon, with only his upper limbs developed. Aruna cursed Vinata to be a slave until the other egg was hatched and her second son could free her. Vinata becomes a slave to Kadru, and once Garuda is born he seeks to free his mother. Kadru wants an immortality drink [Amrit] from the Gods.
Garuda defeats the gods and gets the drink, but doesn’t drink any for himself. Vishnu is impressed with Garuda‘s restraint and asks him to be his vehicle, and grants Garuda immortality. Indra, one of the gods, doesn’t want the nagas to get ahold of the Amrit, so they come up with a plan to trick the serpents. In this exchange, Indra agrees to let nagas be Garuda’s food, dubbing Garuda eater of serpents.
Garuda brings the Amrit in a vessel to the nagas, thus freeing his mother from slavery. He tells the nagas that they need to purify themselves in the river before drinking and while they’re gone, Indra removes the vessel.
(This is a brief synopsis of a story told in the Mahabharata)
The next time you’re challenging yourself in Garudasana, remember who this pose is named for: Garuda, King of Birds