。
She sent me an urgent telegram.
Literal
She [topic-は] me [to-に] urgently telegram [object-を] hit [toward me-てきた].
電報を打つ is the standard verb collocation for sending a telegram — literally 'to hit a telegram,' from the days when telegrams were transmitted via the rapid 'tapping' of Morse code or telegraph keys. The verb 打つ also collocates for typing (キーボードを打つ) and sending text-by-key. The auxiliary ~てくる here marks the direction: she sent it toward the speaker. 至急 ('urgent, immediate') is a sharp formal adverb common in business and emergency contexts. Telegrams (電報) themselves are an artifact of pre-mobile-phone Japan — used for urgent news, congratulations on weddings, or condolences — but the verb 打つ has lived on in 'hit a key' contexts.