Kaepora Gaebora (offically named and introduced in the OoT) is an essential part of many of
Link's quests, OoT being the most visible example. Kaepora had a useful role in other stories, such as
Link's Awakening, by pointing the way to the next dungeon or objective. His relationship to the talking stone statues is unclear, but in
Majora's Mask he has a clear relationship to the statues scattered across the overworld.
In OoT he is strong enough to carry young Link through the air, and can do so repeatedly in certain locations, such as the top of Death Mountain down to Kakariko Village and also from Lake Hylia to the drawbridge just outside Hyrule Market.
Relevant Quotes
Ocarina of Time
According to a gossip stone:
They say that the owl named Kaepora Gaebora
is the reincarnation of an ancient Sage.