To understand the depth of this concept, let us learn the holy words of the Tiferes Shlomo (Parashas Ki Sisa) on the pasuk (Shemos 33:19) וחנתי ארחם, אשר את ורחמתי אחן אשר את I shall show favor when I choose to show favor, and I shall show mercy when I choose to show mercy. Chazal tell us (Berachos 7b) that Hashem will show favor and mercy even to those who aren’t worthy—such is the middah of ורחום חנון to which the pasuk refers. (The חנון expression of Hashem’s kindness is one that goes beyond chessed and rachamim. We invoke it over and over, in Selichos and in the Kedushah of Kesser, because this middah grants favor and mercy even to those who don’t deserve it.)
Says the Tiferes Shlomo: From this Gemara we can infer that Hashem will show favor and answer the tefillos of one who davens for his fellow, even if he isn’t worthy—and Hashem will show mercy towards the one who is being davened for, even if he isn’t worthy. There is a special provision for being heard when davening for someone else.