Boxing is the sport and the art of punching. As a sport, it’s one of the most popular sports worldwide and is usually competed according to the Marquess of Queensberry Rules. Generally, gloves are worn, grappling is forbidden, and striking with anything but the gloves is forbidden (so there’s no headbutting, elbowing, kneeing, kicking, biting, etc). You’re also not allowed to punch a person on the top or back of their head, and you can’t punch below the belt-line (bladder is slightly too low; groin is clearly too low).
Aside from the popular gloved sport, there are also bareknuckle boxing competitions and others which include different rulesets. With gloves removed, parrying becomes more viable and more sophisticated, and new risks emerge such as eye gouging.
As an art, boxing has no strict rules, so the eyes and the groin may become prime targets depending on the strategy & etiquette of the practitioner. The generic term ‘boxing’ is also often used to refer to a much broader system of kickboxing where feet, knees, elbows & heads may be used, and sometimes grappling may even be considered part of the same art although it’s very rare that the word boxing would be used to describe an art that incorporates elements of grappling.