Rabbi Julian Sinclairs weekly dip into the dictionary
Zechut, or zechus in Ashkenazi pronunciation, means something between an advantage, a privilege or a reward. Often it is an advantage or honour that is felt to be a reward. You might say, Its a zechus for me to look after you, or It was a zechus to meet the Lubavitcher Rebbe, or Hes so football mad, he feels that the biggest zechus of his life was to be at the 1966 World Cup Final.
Zechut derives from the word zach, meaning pure or clear. (The Torah speaks of shemen zayit zach, pure olive oil.) From there it came to mean to be acquitted or to be right, particularly in a legal case, and then to mean merit or worthiness more generally.
At this time of year in particular, people speak of zechuyot as the accumulated power of good deeds. In the weeks leading up to Rosh Hashanah and Yom Kippur, we try to earn all the extra zechuyot we can.
Maimonides writes, in his Laws of Teshuvah (3:4), that we should act as if we knew that our zechuyot and avonot, sins, were balanced exactly equally. He stresses, though, that we have no idea how, quantitatively, different good and bad actions are weighed: only God knows.
Moreover, we should imagine the world to be in the same state of equilibrium between good and evil. At any moment then, one good action could tip the balance towards good for us and for the whole world.