What are the structures in roots that are responsible for absorbing water and nutrients from the soil called?

The structures in roots that absorb water and nutrients from the soil are called epidermal extensions or root hairs.

Epidermal extensions, also known as root hairs, are small, finger-like projections that extend from the epidermal cells of the root. These extensions greatly increase the surface area of the root and are responsible for absorbing water and nutrients from the soil. The hypodermis is a layer of tissue beneath the epidermis that provides additional support to the root. Epidermal appendages are specialized structures found in leaves, such as trichomes or stomata. 

The endodermis is a layer of cells that surrounds the vascular tissue of the root and helps regulate the movement of water and nutrients into the plant. While the endodermis plays a role in nutrient absorption, it is not the primary structure responsible for it, as that role is played by the epidermal extensions.