This summary is not the rule. The rule text controls.
If you are convicted of a crime and think your sentence is too harsh, you have the right to ask a higher court to look at it. This right belongs to the defendant. The State (the prosecutor's side) cannot start an appeal just because it thinks a sentence is too light, though it can respond if the defendant appeals first.
When a higher court reviews a sentence, it does not automatically agree with the trial court just because the sentence followed the law. Instead, the court takes a close look at two things: what happened in the crime itself, and what kind of person the defendant is based on their background and history. If the court decides the sentence does not fit those two things, it can change the sentence to something it feels is more fair.
This means a legal sentence is not always a final one. Even if a judge followed all the rules when handing down a sentence, a higher court can still step in and adjust it if the punishment seems out of line with the crime or the person who committed it.