Hangnail

A hangnail or agnail (also known as a stepmother's blessing) is a small, torn piece of skin, more specifically eponychium or paronychium, next to a fingernail or toenail.

Daily use of hand lotion or hand cream may help prevent the formation of hangnails.

For home treatment, the American Academy of Dermatology recommends washing the hands, clipping the loose piece of skin with a clean nail clipper or nail scissors, and applying over-the-counter antibiotic ointment if the area appears inflamed. Persistent hangnails should be evaluated by a physician.

Hangnails can become infected and cause paronychia, a type of skin infection that occurs around the nails. Treatments for paronychia vary with severity, but may include soaking in hot salty water, the use of oral antibiotic medication, or clinical lancing. Paronychia itself rarely results in further complications but can lead to abscess, permanent changes to the shape of the nail or the spread of infection.

...
Wikipedia