We call them noun clauses, which is a group of words that function as a noun in a sentence or phrase. The clause contains a subject and a verb, but it's not a complete statement. (Or as the grammarians like to say, it's a subordinate clause.) Therefore, it has to be connected to an independent clause (main clause). The noun clause usually appears after the main verb of the sentence.
The most common noun clauses begin with that. Others are how, what, whatever, when, where, which, who, whoever, and why.
Here are examples of noun clauses using that.
1. I thought that the test was simple. The noun clause is the object of the verb thought. Ask yourself, Thought what?
2. He proved that he was strong. (The noun clause answers the question, "Proved what?")
3. Sometimes we omit that, but it's implied: He heard (that) she might visit.