If you look at the city view you can see what tiles your citizens are on. You can move them around to tweak production in your city. That's what a worked tile means.
Like if you have one tile with one food (apples?) and one with three that means a citizen on that tile will generate more food for your city. That's what farms or mines or whatever do.
You can work any tiles in the city boundary. Roads are a separate improvement.
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