1) The forty days between the beginning of the month of Elul and Yom Kippur are days of acceptance. Even though Hashem will accept repentance from those who repent sincerely the whole year around, these days are nevertheless chosen specially and ready for repentance, to be days of mercy and acceptance. (Kitzur Shulchan Aruch 128)
2) 2) The reason that these days are days of mercy and acceptance is because our teacher Moshe ascended to heaven on the first day of Elul to receive the second set of tablets, and he stayed there for forty days, and on Yom Kippur Hashem forgave Klal Yisrael for the sin of the golden calf. Ever since, these days have been sanctified as days of acceptance, and the tenth of Tishrei has been set aside as Yom Kippur. (ibid)
