Well... A long, long, long, seriously long time ago, humans received bending, temporarily, from the Lion-Turtles for when they went out into the wild - where the spirits were. And then they would return them.
But the first Avatar, Wan, he managed to get all four of the elements from four different Lion Turtles, and then also accidentally broke up a fight between light and dark itself, and as a result he guarded the light spirit, Raava, until, finally, his soul fused with hers in order to protect her -- and that's how he became the Avatar.
So... It's a human and a spirit combined. That's why the Avatar is the bridge.