This summary is not the rule. The rule text controls.
When someone appeals a conviction from justice court or municipal court, they first need to file a written notice of appeal with the circuit clerk. They also need to post the required bonds or cash deposits, unless the court excuses them from this step. Once these papers are filed, the original conviction is put on hold. It doesn't count against the person while the appeal is happening.
The appeal itself works differently than most appeals. Instead of just reviewing what happened in the lower court, the circuit court holds a brand new trial. This is called a trial de novo. The case starts over, and both sides present their evidence again as if the first trial never happened.
One more detail matters here. If the most jail time someone could get is six months or less, the case can be decided by a judge alone. There's no requirement for a jury in these lower-level cases.