I read a blog post about carotid artery dissection. but i'm still not clear - what is it?

A tear: It is a tear in the wall of one of the arteries that transport blood to your brain. The layers of the wall separate and flap in the blood stream which may cause a cessation of blood supply to teh brain from that artery.

Separation: A normal artery is composed of three layers tightly bound together. A dissection is when those layers "come unglued" . They separate allowing blood to flow between the layers in the wrong space. The artery wall may weaken further and degenerate or the dissection/separation may obstruct branch arteries leading to lack of blood flow down the branches.