Acne vulgaris is the medical name for common acne -- the presence of blackheads, whiteheads, and other types of pimples on the skin. The most common spots for breakouts are the face, chest, shoulders, and back.
Apigee is an API Management tool. If you're interested in API Management systems in general you might find it useful to look at IT Central Station where real users have reviewed many of the options presently available: Best API Management And What Is API Management.
API stands for Application Programming Interface, i.e. API is the way for an application to interact with certain system/application/library/etc. For example, there are API's for OS (WinAPI), API's for other applications (like databases) and for specific libraries (for example, image processing), etc. APIs are usually developed in a form consumable by a client application.