Definition of that conjunction from the Oxford Advanced American Dictionary

     

    that

     conjunction
    conjunction
    NAmE//ðət//
     
    , NAmE//ðæt//
     
     
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  1. 1used after some verbs, adjectives, and nouns to introduce a new part of the sentence She said (that) the story was true. It's possible (that) he has not received the letter. The fact (that) he's older than me is not relevant. In spoken and informal written English that is usually left out after reporting verbs and adjectives. It is less often left out after nouns.
  2. 2so… that… used to express a result She was so tired (that) she couldn't think straight. In informal English that is often left out.
  3. 3(literary) used for expressing a hope or a wish Oh that I could see him again!
See the Oxford Advanced Learner's Dictionary entry: that