You're in your car driving and talking to your friend on the telephone. She comments that she hears a siren in the background. You explain that you're driving through an area with a lot of crime:
I'm driving through a rough part of town.
When you're in an area and driving to a different place, you can say that you're "driving through" that area:
I was driving through New York on my way to Boston.
A "rough" neighborhood or a "rough part of town" is an area where there is often a lot of crime like robberies and murders. You can usually tell that a neighborhood is rough when there are a lot of old, worn-out buildings.
Since rough neighborhoods have a lot of crime, you can often hear police and ambulance sirens. That's why the speaker says "I'm driving through a rough part of town" to explain the siren noise in the background.
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