Cincinnatus was George Washington's role model because he was a citizen of Rome who came to Rome's rescue when he was needed but who gave up power voluntarily and went back to his farming when the crisis was over.
Cincinnatus was offered the dictatorship of Rome by the Senate so that he could lead an army to rescue another Roman army that was in grave danger. He accepted the offer and successfully rescued the trapped army. After that, he could have held on to power through his popularity. However, with the crisis over, he resigned and went back to his farm.
Washington saw Cincinnatus' actions as an example for how he should act. This was why he did not seek power after the Revolution and why he did not try to seek a third term as President later on.