。
She started writing essays.
Literal
She [topic-は] essays [object-を] write began.
随筆 (ずいひつ) means 'essay' or 'personal essay' — a form of Japanese literary nonfiction with a long tradition going back to works like 枕草子 and 徒然草. 書き始めた uses the ~始める suffix: 'began to write.' The sentence could describe the start of a writing career or a new hobby.