While saying this important prayer, we are not to be distracted by anything around us. Closing our eyes enhances our concentration. (Code of Jewish Law, Orach Chaim 61:5)
The Talmud (Berachot 13b) traces this practice to the great Rabbi Judah the Prince. He would often interrupt his Torah lectures for Shema, and his students would observe him passing his hand over his eyes at the moment that he said the verse.
A deeper answer: The meaning of the Shema goes way beyond the belief in only one G‑d. “Hashem Echad” declares that there is no existence outside of G‑d.
Our world, and everything inside it, is created from G‑d’s speech at every given moment. For a few moments every morning, we close our eyes and live this reality.
There is a further possibility that we can offer. At the incident of Moshe encountering the burning bush, we read:
2 And the Angel of the LORD appeared to him in a flame of fire from the midst of a
bush. So he looked, and behold, the bush was burning with fire, but the bush was
3 Then Moses said, "I will now turn aside and see this great sight, why the bush
does not burn."
4 So when the LORD saw that he turned aside to look, God called to him from the
midst of the bush and said, "Moses, Moses!" And he said, "Here I am."
5 Then He said, "Do not draw near this place. Take your sandals off your feet, for
the place where you stand is holy ground."
6 Moreover He said,"I am the God of your father — the God of Abraham, the God of
Isaac, and the God of Jacob." And Moses hid his face, for he was afraid to
look upon God.
In reverential awe, we cover our eyes and look down in order to enhance our concentration, for we serve an awesome and holy God!