Use the noun brush when you want to refer to a quick, light touch. If you are comforting someone you don't know well, you can give their arm a quick brush to show sympathy.
The noun brush can refer to a thick growth of scrub vegetation. You'll have to clear away the brush if you want to plant a garden there. As a verb, brush can mean to sweep, either literally or metaphorically. You can brush the dirt from the floor, but you can't just brush away your past misdeeds. The verb also means to touch lightly. If you are baking and you brush your hand across your cheek, chances are you'll leave a trail of flour there.