Real Dictionary

that conjunction and relative pronoun uses
conjunction: You can use that after many verbs, adjectives, nouns, and expressions to introduce a clause in which you report what someone has said, or what they think or feel.

that demonstrative uses
pronoun: You use that to refer back to an idea or situation expressed in a previous sentence or sentences.

that in American English
the person or thing mentioned or understood
pronoun: (used to indicate a person, thing, idea, state, event, time, remark, etc., as pointed out or present, mentioned before, supposed to be understood, or by way of emphasis)

that in British English
used preceding a noun that has been mentioned at some time or is understood