The word that is used as a conjunction to connect a subordinate clause to a preceding verb. In this construction that is sometimes called the "expletive that." Indeed, the word is often omitted to good effect, but the very fact of easy omission causes some editors to take out the red pen and strike out the conjunction that wherever it appears. In the following sentences, we can happily omit the that (or keep it, depending on how the sentence sounds to us):
Isabel knew [that] she was about to be fired.
She definitely felt [that] her fellow employees hadn't supported her.
I hope [that] she doesn't blame me.
Sometimes omitting the that creates a break in the flow of a sentence, a break that can be adequately bridged with the use of a comma:
The problem is, that production in her department has dropped.
Remember, that we didn't have these problems before she started working here.
As a general rule, if the sentence feels just as good without the that, if no ambiguity results from its omission, if the sentence is more efficient or elegant without it, then we can safely omit the that. Theodore Bernstein lists three conditions in which we should maintain the conjunction that:
When a time element intervenes between the verb and the clause: "The boss said yesterday that production in this department was down fifty percent." (Notice the position of "yesterday.")
When the verb of the clause is long delayed: "Our annual report revealed that some losses sustained by this department in the third quarter of last year were worse than previously thought." (Notice the distance between the subject "losses" and its verb, "were.")
When a second that can clear up who said or did what: "The CEO said that Isabel's department was slacking off and that production dropped precipitously in the fourth quarter." (Did the CEO say that production dropped or was the drop a result of what he said about Isabel's department? The second that makes the sentence clear.)