It means that they were charged with one instance of aggravated assault. Sometimes, a person might fact more than one count, for example, ct. 1 DUI, ct. 2 DLS, ct. 3, leaving the scene. And/or a person might face more than one count of the same crime, e.g., Ct 1 A & B vs Joe, Ct 2 A &B vs Mary. Usually, if there are separate incidents, there will be separate cases, but it could be counts. SO, one count Agg Assault is a charge of a single alleged incident.
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A "Count" is just one "charge". The prosecutor may charge many "counts" in a crime. It is the way the charges or crimes are numbered in the indictment or accusation.
It means a charge. One count equals one charge. If you had, say, 5 counts of Aggravated Assault, it means you are charged with five separate offenses of the crime and could be punished for each separately, which is up to 20 years in prison for each count of Aggravated Assault, or 100 years. One count is one offense they have accused the person of, and the maximum sentence is up to 20 years in prison.