What is the term for a painful, red swelling due to an infection?

The term that describes a painful, red swelling due to an infection is commonly known as an abscess. An abscess is a localized collection of pus that can form as a result of an infection. This occurs when bacteria invade the tissues, triggering an immune response. The body’s defense mechanisms respond by sending white blood cells to the affected area, leading to inflammation, swelling, and pain, which characterizes the abscess.

Infection leads to the accumulation of pus, which is why an abscess appears swollen and tender. Treatment often involves drainage of the pus and sometimes antibiotics to clear the infection.

Other terms like cysts, boils, and furuncles have different meanings. A cyst typically refers to a closed sac containing fluid or semi-solid material, often not associated with infection. A boil is actually another name for a furuncle, which is a specific type of abscess that occurs around a hair follicle, usually resulting from bacterial infection, but the more general term for a collection of pus is what makes "abscess" the most accurate choice for describing the situation depicted in the question.