She is famous in both Japan and America.

Literal

She [topic-は] Japan [as well-でも] America [as well-でも] famous is.

X-でも Y-でも is the 'both / and' construction: 'in both X and Y.' The two でも mark each member as universally true. ~である is the literary copula — slightly more formal than the spoken だ, common in writing about facts and reputations.