She told him, "Please mail this letter."

Literal

She [topic-は] he [to-に] this letter [object-を] please-mail [quotative-と] said.

A direct quotation, set off by the comma before と + 言う (the function of the Japanese 「」 quotation marks here implicit). 投函する is the specific verb for mailing a letter — literally 'to drop into the receptacle' — distinct from the broader 送る ('send'). ~てください makes this a polite request.