。
She is proud of her looks.
Literal
She [topic-は] her own appearance [object-を] is-boasting-about.
容貌 (ようぼう, 'facial features, looks') is a more formal/literary word for someone's facial appearance — it feels clinical or written rather than spoken, and slightly more formal than the everyday 容姿 ('appearance, figure') or 顔 ('face'). 自慢する takes its object with を and means 'to be proud of, to boast about.' The progressive ~ている marks this as an ongoing attitude rather than a one-time act of bragging.