Final answer:
The medical term for pertaining to under the skin is 'subcutaneous.' The hypodermis serves as the connecting layer between the skin and the underlying tissues, while the dermis is the core of the integumentary system with many vital functions.
Step-by-step explanation:
The medical term for pertaining to under the skin is subcutaneous. The hypodermis, also known as the subcutaneous layer or superficial fascia, is the layer directly below the dermis. This layer serves to connect the skin to the underlying fascia of bones and muscles, and is not strictly part of the skin, although the border between the hypodermis and dermis can be difficult to distinguish. The hypodermis consists of well-vascularized, loose, areolar connective tissue and adipose tissue, which functions as a mode of fat storage and provides insulation and cushioning for the integument. The dermis itself might be considered the "core" of the integumentary system. It contains blood and lymph vessels, nerves, and other structures, such as hair follicles and sweat glands, and is made of an interconnected mesh of elastin and collagenous fibers, produced by fibroblasts.