。
She has an impressive background.
Literal
She [topic-は] wonderful career-history [object-を] has.
経歴 (けいれき) means 'career history' or 'professional background' — the sum of someone's experience and accomplishments. 持っている (literally 'is holding') is used in the sense of 'to have' or 'to possess' when talking about qualifications, records, skills, or other abstract possessions.