。
She's embarrassed about her old clothes.
Literal
She [topic-は] old clothes [object-を] is-showing-shyness.
恥ずかしがっている applies the suffix ~がる to the i-adjective 恥ずかしい ('embarrassed, ashamed'), turning it into a verb 'show signs of being embarrassed.' Japanese normally restricts direct emotion adjectives to the speaker's own feelings — you can't simply say 彼女は恥ずかしい to describe someone else's state. The ~がる workaround says 'is exhibiting the outward signs of feeling embarrassed,' moving from inner state to observable behaviour. The を marks what triggers the embarrassment, with the ~ている giving an ongoing-state reading.