What is the slender threadlike outgrowth of the skin that covers the head and body?

The slender threadlike outgrowth of the skin that covers the head and body is best described by the term "hair." Hair is a filamentous structure composed primarily of keratin, a type of protein. It grows from hair follicles, which are embedded in the skin. This structure is unique to mammals and serves various functions, including protection, thermal insulation, and sensory perception.

When discussing the other options, while nails are also outgrowths of the skin, they are found on the fingers and toes rather than covering the entire body like hair does. The hair shaft refers specifically to the visible part of the hair that extends beyond the skin's surface, but it does not encompass the entirety of the hair structure, which includes the follicle beneath the skin. Fur usually refers to the soft, fine hair covering the bodies of animals; it is a term that doesn’t adequately describe the general structure found on human heads and bodies. Therefore, hair is the most accurate term that encompasses the slender, threadlike outgrowth as described in the question.