That is an innocuous little word, but it is often a linchpin of comprehension, making the difference between understanding and confusion. Take, for instance, its insertion or omission as a conjunction following verbs such as believe, ensure, and indicate.
In the sentence “The seizure of the port will ensure command of the sea and free lines of communication,” a conjunction after ensure would make no sense; the sentence clearly states that an action will guarantee two results. However, a rewriting of the sentence changes the game. Here, it is correct to insert that: “The seizure of the port will ensure that we maintain command of the sea and free lines of communication.” (It’s not required, but it is recommended for a more smoothly flowing sentence.)
Sometimes, though, the omission of the optional that is not so optional; withholding it can hinder comprehension. For example, in the sentence “I hope to ensure that his arrival does not affect our plans,” withholding that after ensure might deceive the reader into thinking that the sentence consists of the simple statement “I hope to ensure his arrival,” but he or she must then must shift gears to absorb an extended phrase that expresses a purpose. In this case, it’s almost an obligation to the writer to insert that after ensure: The reader’s train of thought is interrupted when he or she continues past the putative predicate. Insertion of that after ensure will guarantee that the reader is not derailed.
Likewise, while reading the sentence “She glared at him, unable to believe what she had heard was coming from a friend she had trusted,” the reader might believe that the sentence consists only of the statement “She glared at him, unable to believe what she had heard.” To clarify that additional information is coming, it’s best to include that after believe: “She glared at him, unable to believe that what she had heard was coming from a friend she had trusted.”
This assistance isn’t always essential; the sentence “I believe intervention is the wiser course” would not be initially misinterpreted as a sentence that might end at intervention. However, as a courtesy to your readers, consider always including the optional conjunction.
What if you started to read a sentence beginning with “He pointed his chin to indicate the chair to his left”? You might expect that clause to be self-contained. But if the statement continues “had been left vacant for her,” you’d probably wish that indicate had been followed by that to signal that more is to come. Such details distinguish competent writing from commendable writing.