‘Elohim (אלהים) is morphologically plural, but as everyone knows, it’s frequently used in reference to singular subjects (primarily the God of Israel). The Bible is not the only place this happens, though. The Akkadian word for “gods,” ilanu, frequently occured in reference to singular subjects in the Amarna Letters (almost always in correspondences written by Syro-Palestinians to Egyptians), in Akkadian texts from Ugarit, and at Taanach and Qatna. The Phoenician ‘lm is used the exact same way. This usage predates the appearance of this phenomenon in Biblical Hebrew and is no doubt at the root of it. The distribution of this kind of usage moves from the coast to the valleys and then to the highlands.
We know from patterns in the languages in which this phenomenon occurs that it most likely derives from the abstract plural. This is the expression of an abstraction through the plural form of the noun or adjective. We see this in Hebrew with ‘abot, “fatherhood,” the plural of ‘ab, “father,” and zequnim, “old age,” the plural of zaqen, “old,” among many others. Some of these terms were used in reference to an individual entity or object that exemplified the quality of the abstraction. For instance, in Dan 9:23 Gabriel tells Daniel that he is a hamudot, which, as an abstract plural, means “desirableness,” or “preciousness.” In this instance, the abstract should be concretized in reference to Daniel. He is not “desirableness,” but one who exemplifies that quality. He is highly esteemed. Joel Burnett suggests “concretized abstract plural” as a designation for this usage. The word ‘elohim still retains its other uses (the simple plural, etc.), but can be used to refer to singular subject. ‘Elohim, then, means “divinity,” or “deity.” The God of Israel exemplifies divinity.
For a more complete discussion, the best treatment is Joel Burnett, A Reassessment of Biblical Elohim (Atlanta, Ga.; Society of Biblical Literature, 2001), 7–24.