This meaning refers to drawing attention to something one is proud of, often in an annoying way.
He bragged about winning the competition.
She never brags about her success.
As a noun, brag refers to a statement expressing excessive pride or superiority.
His claim sounded like an empty brag.
The advertisement was full of bold brags.
This uncommon use refers to something a person or group takes special pride in.
The garden was the family's chief brag.
The new stadium became the city's brag.