The word "God" here is Elohim. It says, "The LORD our Elohim is one LORD." This phrase is not normally grammatically correct—a plural noun [Elohim] with a singular verb, "is." Elohim is the plural of both El and Eloah. El and Eloah mean "mighty One," "strong One," or "powerful One" according to Brown, Driver, and Briggs. Elohim, being either of these two words in the plural, therefore means "strong Ones," "mighty Ones," or "powerful Ones."
Just from these definitions, Elohim consists of at least two powerful beings. But, as the New Testament shows, Elohim is not limited to two. It can actually signify an unlimited number, so Elohim is a group or assembly of powerful beings.
It is jarring to the ear to say "Gods is," because there is a plural noun and a singular verb, but it is not incorrect. Consider "United States of America." States is plural, but one does not say, "The United States are going to war." One says, "The United States is going to war." One uses a singular verb with a plural noun. Gramatically, we are speaking of collective nouns.
Elohim is plurality in one, and because the sense is singular, it calls for a singular verb. However, everyone using it knows that it is plural and represents many in unity. Our culture forces us to look for a singular being, but Elohim is not singular.
In the New Testament, it becomes very clear that Elohim is a kingdom, consisting of many! Elohim always acts in a singular way. There is never any divisiveness, only agreement.
We have no problem at all saying or hearing, "The United States is bordered on the north by Canada," or, "The United States is in the northern hemisphere," or "The United States delivered a sharp memo to the Japanese today." We always speak of the United States in the singular. We speak of it as a composite of many rather than a singular entity.
When Moses wrote this verse, it was no more discordant to a Hebrew-speaking person, no more grammatically wrong, than it is for us to say, "The United States is. . . ." Elohim, "the powerful Ones," is a Family of at least two divine beings, and many sons and daughters coming into it. A family, whether human or divine, is a unit of many individuals joined as one.
The Bible reveals that a nation is nothing more than a family grown great. This is why we have the Table of Nations in Genesis 10, which shows the forebears of the nations after the Flood. They began with one man and one woman, and they grew great. So it is that Elohim is one institution—a Family—growing ever larger and more complex until it becomes a nation, the Kingdom of God. We see, then, that this is what Elohim is developing.