Please accept my humble obeisance. All glories to Srila Prabhupada
Vishnu's divine vehicle is Garuda, a giant eagle, often depicted as having a human body and senses and bird-like forehead, wings, beak and nails. He wears a crown on his head like his master, Vishnu. His stature in Hindu religion can be gauged by the fact that an independent Upanishad, the Garudopanishada, and a Purana, the Garuda Purana, is devoted to him. Various names have been attributed to Garuda - Chirada, Gaganeshvara, Kamayusha, Kashyapi, Khageshvara, Nagantaka, Sitanana, Sudhahara, Suparna, Takshya, Vainateya, Vishnuratha and others.
The Vedas provide the earliest reference of Garuda, though by the name of Shyena, where this mighty bird is said to have brought nectar to earth from heaven. The Puranas, which came into existence much later mention Garuda as doing the same thing, which indicates that Shyena and Garuda are the same.
Garuda was born of sage Kashyapa and his wife Vinata. It is said that Valakhilyas - the group of 60000 thumb-sized sages - handed over the fruit of their great penance to sage Kashyapa, who in turn handed it over to Vinata - his wife. Vinata then bore an egg, directly from which arose Garuda, complete with huge wings. One of the most popular tales of Garuda describes his stealing the divine nectar of immortality or amrit from heaven. Garuda's mother Vinata was enslaved by Kadru, his step-mother, when Vinata lost a wager to Kadru, albeit through deceit, perpetrated by Kadru. Kadru asked for Amrit as ransom to release Vinata. On hearing this Garuda reached Indra's capital Amravati in search of Amrit. Indra's armies of Gods tried to stop Garuda but he defeated them all along with all other divine forces which tried to stop him from reaching the divine well holding the nectar of immortality. He brought the nectar with him to his step-mother, Kadru but answered Kadru's deceit with his own and without handing over the nectar, got his mother, Vinata, released. Vishnu had noticed the proceedings and was impressed by Garuda's honesty in that he had not once touched the nectar that he was carrying for so long. Vishnu requested Garuda to become his vahana or vehicle, to which Garuda agreed but put forth two conditions - one that he be held higher to Vishnu and second that he became immortal without drinking the immortality nectar. Vishnu granted his two wishes. Vishnu placed Garuda atop his flagstaff to fulfill his wish of being placed higher than Vishnu. Thus was born the concept of a Garudadhvaja - or a flagstaff with Garuda adorning the top. Every Vishnu temple has such a Garudadhvaja in front of the sanctum - a tall pillar (Dhvaja), with Garuda enshrined upon at a position higher than that of the idol of Vishnu.
Hindu art depicts Garuda with a serpent on his chest. There is an interesting tale leading to this symbolization. Garuda became arrogant with his new found position atop Vishnu along with immortality. Once, Indra, the king of Gods, granted the serpent Sumukha the boon of immortality. Garuda, being half eagle, looked upon serpents as his food and felt that Indra's boon to Sumukha was an affront to him since Sumukha being a serpent, was his enemy and food. Garuda therefore quarreled with Indra and in the process of doing so boasted that he was mightier than even Vishnu and that is why he was placed higher than Vishnu. As punishment for his arrogance, Vishnu pressed one of his fingers on Garuda's person. Garuda felt an unbearable pain and begged Vishnu for relief. Vishnu relented but to remind Garuda of his mistake of arrogance, placed Sumukha on his chest like a garland.