Why Garuda eats the Nagas (Serpents)
In the Mahabharata the great archenemy of the Nagas (serpents) is the massive eagle-king Garuda. Garuda and the Nagas were actually step-brothers. The sage Kashyapa had 13 wives; all were prajapati Daksha's daughters. One of them, Kadru desired many children while another, Vinata desired few but powerful offspring. Kasyapa, on the pleadings of his wives, granted them their wishes. Kadru laid a thousand eggs which hatched into snakes or the Nagas. Vinata on the other hand laid two eggs but they did not hatch for a long time. Impatient, Vinata broke open one egg, which was half formed. Her half-formed son cursed her, decreeing that she would be a slave for her sister for a long time. Later her second son will come to rescue her from this curse. Her first son then became Aruna, the red spectacle seen as the Sun rises in the morning; he became charioteer of the Sun. When the second egg hatched, a fully grown, shining and gigantic sized bird form emerged as Garuda, the king of birds.
Vinata lost an unwise bet to Kadru, and became enslaved to her sister. As a result Vinata's son Garuda was required to do the bidding of the Nagas. Resolving to release his mother from this state of bondage, Garuda approached the serpents and asked them what it would take to obtain her freedom. Their reply was that Garuda would have to bring them the elixir of immortality or Amrita.
It was an enormous task as the amrita was in the possession of the Devas. They guarded it zealously since it was the source of their immortality. Garuda defeated all the defenses setup by the Devas to protect the Amrita. He then held the Amrita in his beak and flew towards the Nagas. On his way, he encountered Lord Vishnu. Rather than fighting, the two exchanged promises. Vishnu promised Garuda the gift of immortality even without drinking from the elixir, and Garuda promised to become Vishnu's mount.
Then Garuda brought the Amrita to the serpents to fulfill their condition, but through a deception prevented them from consuming it and achieving immortality. The Nagas were tricked to perform a holy bath before consuming the Amirita. In the meantime Indra swooped in to make off with the elixir. From that day onwards, Garuda was the ally of the gods and the trusty mount of Vishnu, as well as the implacable enemy of the Nagas, and prayed upon them on every opportunity.
Source of info: Book I: Adi Parva, Sections 16ff