Final answer:
The term used to describe an acute painful nodular inflammatory process of the eyelid is a stye, also known as a hordeolum.
Step-by-step explanation:
The term used to describe an acute painful nodular inflammatory process of the eyelid is a stye. A stye, also known as a hordeolum, is a red, painful lump that forms either inside or on the surface of the eyelid. It is caused by a bacterial infection of an oil gland in the eyelid and can be associated with symptoms such as redness, swelling, and tenderness.