One of the regular functions of と in Japanese is as a quotation particle. This use is called 引用（いんよう） in Japanese, which basically translates as ‘reference’, or ‘citation’. This way of using と can appear after almost any type of word (or phrase), but requires だ when used after nouns or な-Adjectives.

• 先生（せんせい）が「危（あぶ）ない！」と叫（さけ）んだ。
  The teacher yelled, ‘Watch out!’
• 木村（きむら）さんが「3キロ歩（ある）いた」と言（い）った。
  Kimura san said, ‘I walked 3 km.’
• あれは猫（ねこ）だと思（おも）う。
  I think that is a cat.
• 富士山（ふじさん）は綺麗（きれい）だと思（おも）う？
  Do you think that Mt. Fuji is beautiful?

と as a quotation marker will almost always be followed by a verb that shows what type of ‘quote’ it is. This can be words like 言（い）う, 思（おも）う, 考（かんが）える, 聞（き）く, etc. However, at the end of a sentence, the verb will often be omitted.

• 生徒（せいと）が先生（せんせい）に「何（なん）で？」と。
  The students asked the teacher, ‘Why?’

As with other instances of the particle と being used, this use simply expresses the relationship between (A) ‘what was communicated’, and (B) ‘how it was communicated’.