Why make this change?

The story (or the scene) is written from the point of view (POV) of a particular character. We can only know what he or she knows. Therefore, anything felt, seen, heard, or smelled is, by definition, something the character felt. So you don't have to tell us that he or she felt it. It's understood.

If you rewrite accordingly, your writing will be much cleaner without a lot of extra words. Consider:

He walked into the square and heard the bells ringing.

There are many ways that this (or any) line can be rewritten. Is it necessary, though, to tell us that he heard the bells? No. Of course he heard the bells. If he had not heard the bells, we would not know they were ringing. 

The bells rang as he walked into the square.

As he walked into the square, the bells rang.

He walked into the square. The bells of the church began to ring.

There is no right or wrong way. Even saying that he heard them is not patently wrong. You will find many examples, particularly in popular literature. I only suggest that it's not necessary to tell us that the character heard, smelled, saw, or felt something. Just give us the sight, sound, feeling, or smell.

Why make this change?

"Angrily" is an adverb. It modifies a verb. But what does it mean? What image does it conjure in your mind? I don’t think it brings any image to mind. Why not? Because it could mean anything. Maybe he yelled. Maybe he whispered it because that’s how he reacts when he gets angry. Maybe he punched a hole in the wall. But as it is, it doesn’t tell us much.

Using an adverb is telling, not showing. It’s lazy writing. Elmore Leonard (Get Shorty; Rum Punch) refused to use them.

Consider instead the change I made by way of illustration. We have something we can see. He pounded the table. His face is red and he’s practically foaming at the mouth. We’re not told he was angry, we are shown it. We see it in our mind’s eye.

There are certainly times when you have to tell, not show. The trick is to learn when to do each. The amateur writer will sprinkle adverbs around like fairy dust. 

Go through and hunt for adverbs. They end in “ly.” If there is an “ly” word, try to find a way to describe what you’re trying to convey by using that word. 

Take our example of “angrily.” What do people do when they say or do something angrily? What gestures do they make? How is their face changed? How is their manner of speech changed?

They throw their hands in the air; they pound the table or punch the wall; they throw things; they shout; their face turns red; they may cry; they may give a primordial scream. I could go on and on. And so could you.

Replace “ly” words with active descriptions and watch your writing improve.

Why make this change?

You've heard it a million times. "Show, don't tell." But what does it mean? Consider the example above. You can either tell me it was a nice day, or you can provide a description showing me what the weather looked like, and I will know that it was a nice day.

Now, everything cannot be be showing. There must be an element of telling. You can tell me that the character picked up a pencil, or that he opened the window and the sun was out. Generally, however, you should avoid it in the narrative.

Look through your own writing and you will more than likely find telling where you should be showing. For example,

He was a handsome man.

What does that tell me? Nothing. The reader has to process in his or her mind what that means. If, on the other hand, you were to write:

His deep blue eyes shown from a tanned face with rugged features that must have been chiseled from stone.

Then the reader has something they understand. I don't warrant that my rewrite of that line is going to win any literary awards, but it is much more interesting that just saying he's handsome.

Consider another example:

She had on nice clothes.

What does that tell me? Again, nothing. It depends on what you mean by nice. So,

Well, I'll let you do the work. How would you, in the context of your story, describe the clothes the woman had on?

Delete semicolons and exclamation points.

Why make this change?

There are two reasons. One is that they are hallmarks of the amateur writer. New and  amateur  writers throw around semicolons and exclamation points like candy. The other is that you more than likely don't know how to use a semicolon.

Kurt Vonnegut said that all using a semicolon does is show that you went to college.

I think all they mean is that you went to college, but missed semicolon day in English 101. I rarely see them used properly. In general, people tend to use them in place of commas, which is wrong. Where you use a semicolon, you could just as well use a period. That’s why I say not to use them. Why not just go ahead and use a period?

Go through about any work by a well-known author (By which I mean a real writer, not some schlep). You will certainly find semicolons, but very few. Maybe five or six in the whole novel. And I’m guessing that either they were the few allowed by the editor, or were added by the editor.

If you use them incorrectly, the publisher or agent will know. It will diminish your chances of being published. It shows you really don’t know how to write.

As to exclamation points, it’s a different thing. Everyone knows how to use them. What you should know, is how not to use them. Your novel should contain as few as possible, probably no more that half a dozen. I’ve even seen pundits say there should be no more than two.

Again, go through the work of a well-known author. You will find them, but very few.

What I mean by knowing how not to use them, is that the reader should be able to understand that the quote was an exclamation by the context.

For example, do I need an exclamation point here:

The man grabbed her arm and pulled her toward him.
“Get your hands off me!” she screamed.

Isn’t the exclamation point redundant? Isn’t it clear from the context, and the fact that she screamed, that the statement would have been made as an exclamation? (Say yes.)

The goal here is to look like you know what you’re doing. To look like a professional writer. Look at it this way: an agent or publisher is not likely to say, “I think there should a semicolon here,” or “Wouldn’t this be better with an exclamation point?” They are more likely to say, “Look at all those (incorrectly used) semicolons. Amateur. Next.”

Why make this change?

This is a tricky one. Like “just” or “really,” “that” is often unnecessary. My test is if the sentence is rendered nonsense with “that,” or if the meaning would be changed without it, then keep it. Otherwise, leave it out.

For example:

The President said (that) June 1st the new law will take effect.

Without “that,” the President said it on June 1st.

With “that,” the law takes effect June 1st.

You would include/omit in this case depending on what you want the sentence to mean.

Take another example:

“Which one?”

“That one.”

There’s no question that “that” is necessary for the sentence to have any meaning in the context of the question.

Now, consider my example:

“This is the beer that I like.”

This is a “that” that should be omitted. Is it technically incorrect? No, I don’t think so. But it’s inartful. The sentence has the same meaning with or without it, and without it the sentence still makes sense. So, leave it out.

The best article I found on the use of “that” is here. The author makes a valid point, which is that using “that” is generally not grammatically incorrect, but omitting it might be.

That’s certainly true, but I submit that peppering your work with unnecessary “thats” is worse than leaving one or two out where they arguably should go. Sometimes it’s a judgment call, sometimes it’s a matter of style. Generally, though, they should be omitted, unless it affects the meaning of the sentence, or renders the sentence nonsense.