。
She is boasting about her beauty.
Literal
She [topic-は] her own beauty [object-を] is-boasting.
美しさ ('beauty') is the productive nominalization of the i-adjective 美しい via the ~さ suffix, which converts adjectives into nouns denoting the abstract quality itself. 自慢する ('to brag about, take pride in') takes its object with を. With ~ている, 自慢している reads either as 'is bragging right now' (ongoing action) or 'has the habit of bragging' (habitual) — context decides.