。
She boasts about her good looks.
Literal
She [topic-は] appearance [possessive-の] good thing [object-を] is-boasting.
容姿のいいことを自慢している — 容姿 (ようし, 'appearance, looks') is a formal compound. のいいこと nominalizes the positive quality. 自慢する (じまんする, 'to boast/take pride in') describes someone who openly displays self-satisfaction about an attribute.