It is the tree that acts as a barrier between the real world and Magano. It is said that the first and strongest exorcist, Abe no Seimei, created this. The Exorcist Union built their HQ around the Ame-no-mihashira so they can constantly protect it from attack. The only time that the barriers around the Ame-no-mihashira have been breached is by Kuranashi who stole a branch from it. Sae is the personification of that stolen branch.
Yin and Yang Edit
Ame-No-Mihashira is also said to be emitting yang energy over the course of thousands of years while draining the yin energy from humanity. The energy is suppose to be sent to Abe no Seimei's true body but it flowed into the Adashino clan instead thus accumulating in Benio