What does it mean to change the tone of a piece of writing?

The tone is the author's attitude. You can see this by the way they write: their Word choice, sentence structure, and phrasing. If you change that, you change the tone of the writing.

Let's see an example. Here's one way to explain tone:

Tone is the author's attitude. This is shown by the author's Word choice, sentence structure, and phrasing.

Here's another explanation, with a different tone:

Tone just means how the author thinks, what their attitude is, how they see the world. Look at the way they say things. Look at how they talk to you. Check out their Words and phrases.

See how different Word choices can change how something comes across?