At Beth Immanuel, some people cover their eyes with their hand as they recite the beginning of the Shema: "Hear O Israel, the LORD our God, the LORD is one." This is done to help us concentrate on what we are saying.
Reciting the Shema is known as accepting the yoke of the Kingdom of Heaven upon oneself. When we recite the Shema, we are accepting God as our King every day. We cover our eyes to help us concentrate as we acknowledge that the LORD alone is our God. The next section, "Blessed be the Name of His glorious Kingdom for ever and ever," is recited softly with our mouth covered as a reminder that God's Kingdom is not yet fully established on the earth (and as a reminder that those words are not part of the original text from Deuteronomy).
