。
She said she had met him the day before.
Literal
She [topic-は] previous [possessive-の] day [on-に] him [to-に] met [quotative-と] said.
と marks the preceding clause as the content of what was said — the quotative particle. In indirect speech, the quoted clause stays in plain form (会った, not 会いました) regardless of the overall sentence's politeness level. Note the tense difference between Japanese and English: Japanese uses simple past 会った where English shifts to past perfect 'had met' in reported speech. This lack of tense-shifting makes Japanese indirect quotation structurally simpler than English.