。
She brags about her family.
Literal
She [topic-は] family [of-のこと] [object-を] boasts.
のこと is the softening particle Japanese reaches for when the object of an emotion or attitude is a person or personal relation: ~のこと(を)考える ('think about ~'), ~のこと(を)心配する ('worry about ~'), ~のこと(を)自慢する ('boast about ~'). Literally 'the matter of X,' the のこと preserves the personal connection rather than treating the person as a bare grammatical object. 自慢する is an interesting verb — pride that crosses into bragging, displayed publicly. Whether it lands as warm pride or annoying boastfulness depends on tone and audience.