。
She is just as smart as he is.
Literal
She [topic-は] he [as-と] same [degree-くらい] head [subject-が] is-good.
~と同じくらい is a comparison structure: 'about the same as ~.' 頭がいい ('smart') literally means 'the head is good,' fitting the pattern 'X は Y が ADJ' — the topic 彼女 is the larger subject and 頭 the smaller, embedded subject. This double-subject pattern is sometimes called the '象は鼻が長い' construction.