To get dirty; to become soiled (of objects or places).
子どもたちが泥で服を汚れてしまった。
The children got their clothes dirty with mud.
手が油で汚れているから洗ってきてください。
Your hands are greasy; please go wash them.
壁にペンキが飛んで汚れてしまった。
Paint splattered on the wall and it became stained.
To become sullied or corrupted (reputation, morals), or, in some contexts, to lose chastity; often a stronger, figurative meaning.
そのスキャンダルで彼の評判は汚れた。
His reputation was sullied by the scandal.
長年の汚職で政治家のイメージが汚れてしまった。
Years of corruption have tarnished the politicians' image.