When the bark of a tree is removed in a circular fashion all around near its base, it gradually dries up and dies because

In vascular plants, phloem is the living tissue that carries organic nutrients (known as photosynthate), in particular, glucose, a sugar, to all parts of the plant or particularly non-photosynthetic parts of the plant such as the roots.  Because phloem tubes sit on the outside of the xylem in most plants, a tree or other plant can be effectively killed by stripping away the bark in a ring on the trunk or stem. With the phloem destroyed, nutrients cannot reach the roots, and the tree/plant will die.