As I have mentioned before, my day job concerns technical writing. I am an archaeologist and write technical reports detailing the methods, analytics, and results of archaeological investigations. In this context, "That" is an acceptable word to use. However, in the world of fiction, it is not so acceptable.
For some background, "That" is a versatile word. It is a pronoun, adjective, adverb, conjunction, idiom, and determiner. It is also hollow and distracting to the reader-a filler word.
One of my worst crimes in writing, aside from the overuse of "was," is probably the overuse of "that." To me, it represents specificity, and easily serves many of my purposes. However, it is also a lazy word disallowing me to develop stronger writing skills. The word also changes the voice of what is being written. "That" can change an active voice into a passive one.
"'That' is a lazy word that disallows me to develop stronger writing skills."
In this sentence, "that" dulls the sentence down, becoming more explanatory. There is no action, no life to it.
"'That' is a lazy word disallowing me to develop stronger writing skills."
In this sentence, the 'lazy word' has action. It is doing something. It lives in writing.
As writers of fiction and creators of other worlds, we want to breathe life into our work. Using words like "that" can kill our work. You will find as you go through your text many of the instances of "that" can be easily edited out without affecting the flow of your writing. The added benefit is your writing will be stronger and more active. Trust me when I say your editor will thank you for following this advice.
Mind you, this is not to imply the word "that" is never necessary. Sometimes, due to an explanatory section of prose, "that" could be used effectively without hurting your writing. But in most cases, it would behoove you to revise the text to avoid "that." Keep your writing alive, kill "that."