We cannot truly comprehend Hashem. "His throne is in Heavens above and His powerful presence is in the loftiest heights" (Aleinu). Yet, Bnei Yisroel through their avodah and tefillos, have the ability to bring Hashem down to this physical world.
Chazal tell us (Devarim Raba 2, 6) that idols are close by, but, at the same time, they are really far away. A gentile makes an idol and places it in his house - close by. However, when he prays for help he receives no answer, as if the idol is quite distant. In contrast, Hashem's abode is in the heavens which is a five hundred year journey away. Yet, even a prayer in a person's heart is heard by Hashem, for in reality He is very close by.
Regarding the Torah, the Medrash (ibid. 8, 7) says that Bnei Ysroel asked Moshe, "You say the Torah is not in the Heavens nor is it across the ocean; if so where is it?" To which he responded, "It is in your hearts and mouths - it isn't distant, it is very close." Rav Wolbe adds (Alei Shur vol. II pg. 405) that the very purpose of the Torah is to engender closeness, by bringing Hashem down into our lives. One who begins learning Gemara and studies the laws of a bull goring a cow, might wonder how such a topic is supposed to bring one closer to Hashem. After a while he will begin to realize that there is no aspect of our lives that is not directed by Hashem's will. Every topic in Gemara is a lamp that illuminates and guides us in some aspect of life. Although other nations also believe in The Creator, in their eyes He is entirely metaphysical and abstract, and they don't have the wherewithal to connect with Him.
Even the final redemption is tentatively close at hand. When Bnei Yisroel asked Bilam when the final redemption will take place, he answered "I see it but it is not near" (Bamidbar 24, 17). To which Hashem responded, Bilam does not wish to see My redemption for then he will be severely punished and therefore, he says that the redemption is not near. However, you shall yearn for the redemption since it is close at hand: "Observe justice and perform righteousness for My salvation is soon to come" (Yeshaya 56, 1).
The Torah delineates a number of aveiros that were committed by Bnei Yisroel. However, there were two aveiros that undeniably had the most far reaching ramifications. The first was the sin of the golden calf, whereby Bnei Yisroel lost most of the uniqueness given to them. They lost their great stature (the crowns), the freedom from the death, and the ability to study Torah without forgetting. Additionally, Chazal tell us that any suffering that befalls the Jewish nation includes some of the punishment that was intended for the Jewish people when they worshipped the golden calf. The second aveirah was the sin of the spies. Their derogatory report about Eretz Yisroel caused the nation to cry, and thereafter that day was designated as a day of crying for all generations.
In the Jewish calendar, the days on which these two aveiros were committed, fall out within a mere three weeks of each other. These three weeks are the time designated to contemplate just how far we are from Hashem. In reality, Hashem, the Torah and the final redemption are all within arm's reach; it is our aveiros that cause the distance. This is the time to mourn that distance which was caused by our own actions. This mourning itself has the capacity to minimize this distance.