。
She thinks she's smart.
Literal
She [topic-は] her own self [object-を] head [subject-が] good [quotative-と] is-thinking.
頭がよい ('head is good' = 'smart, intelligent') is one of Japan's classic body-part personality idioms: a quality of the person is expressed as a state of the body part. Other examples in the same family include 頭が固い ('inflexible'), 顔が広い ('well-connected'), 口が軽い ('blabby'). The reflexive 自分の事を + judgment + と思っている is a common frame for 'thinks of oneself as X' — note the matrix subject 彼女 thinks about 自分 (which corefers with 彼女).