The story is told that a woman once came to a rabbi to ask him to be a judge for her bais din (judgment) on a certain matter. The woman became very emotional and began crying. The rabbi said that he could not judge anymore. The reason is because he saw her crying and the tears made him have compassion for her. When a person sees another crying, they always are affected. Therefore, the rabbi said he could no longer be an impartial judge. He has a special connection for the woman’s side and might not rule fairly.
We can compare this to crying when we daven. The Judge in Heaven sees our tears and has compassion for us. He cares more for our cause and has difficulty giving us a negative judgment. Therefore, it is very important to try to use our tears during this time of year to get written and sealed for a good judgment on the upcoming High Holidays.