Make sure the object has UVs and a Material assigned to it.
You also need to have a texture projected onto a model in order to use the UV Brush tool. This tool lets you move the UV texture coordinates by brushing. This is useful when you want to minor edits.
Using UV Brush
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Select your model.
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Click the UV Brush tool on the Texture tab.
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Drag the brush tool over the UVs to move them.
For general brush information see the Brush tool help.
For specific parameter help see the UV Brush