The Gemara on Amud Aleph says:

חֲבִיבִין יִשְׂרָאֵל שֶׁלֹּא הִצְרִיכָן הַכָּתוּב לְשָׁלִיחַ.

The Jewish people are beloved by God, as the Torah did not require them to make use of an agent, e.g., an angel, to intercede on their behalf. Instead, God hears the nation’s prayers directly. Consequently, the High Priest, who represents the people on Yom Kippur, need not approach in a roundabout fashion.

Rashi expands on this:  

Rather, each and every one prays for himself, as each one knows the blemishes that affect his heart.  As Solomon states (Kings I:8:38): Each of whom knows his own affliction—when he spreads his palms toward this House.

Although the beautiful words of the Gemara and Rashi speak for themselves, I will make one observation. The Gemara by itself indicates that the Jewish people have this quality of being able to reach toward God without an intermediary. However, Rashi seems to add a dimension, perhaps his explanation for why this works or how it works. 

If we pay careful attention to what Rashi says, we will note that Rashi adds that each person can see the blemishes within their own heart. I believe this is significant in that Rashi is telling us that the way in which to cause prayer to ascend directly to God without an intermediary. The very power that is contained within the Jewish prayer, is that it emanates from seeing the deficiencies in one’s own heart.