(The "h" has been substituted with a "k" to protect the sanctity of the Names of the Creator.)
Elokim - G-d
The Peshat (plain meaning) of the word is that it describes divinity. It describes the One who possesses all the divine powers. This is the reason it is expressed in the plural, i.e. not merely kel or eloka, but One who comprises all the divine powers within His essence. An example of such use of the word is found in Yehoshua 24:19 elokim kedshim hu which means that in His capacity as elokim He comprises all aspects of holiness, sanctity.
A parallel use of words describing terrestrial authority is found Yeshayahu 19:4, where rulers are described in the plural as adonim kasheh (a harsh master) although the adjective applied to "them" is in the singular. The reason the noun is in the plural is because such rulers manifest their authority in so many different ways. If such use of the plural is appropriate for describing terrestrial rulers, how much more so is it appropriate for describing G-d whose authority is manifest in innumerably more ways than the authority of even the most powerful human king on earth. Their entire authority is, after all, only derived from G-d. G-d, by definition, is One, indivisible, but His powers are many.
There are other examples of nouns in the singular being described as if they had been written in the plural. To name a few: Shemot 12:42: leil shimurim hu (it is a night of vigil), the word for vigil is in the plural. VaYikra 23:28: yom kipurim hu (It is a Day of Atonement).
Another reason why the Torah refers to G-d as elokim in the plural is the great deal of intelligence, wisdom, and insight He employed when He created the universe. This is what Shlomo had in mind when he wrote in Mishlei 3:19, "Hashem founded earth by means of wisdom, He established the heavens by using insight." G-d is described as emplying different attributes when creating the universe.
From a Drash (homiletical) point of view the name elokim describes G-d in His capacity as judge. This is what the Torah meant when it wrote "elokim lo tekalel - you must not curse a judge" (Shemot 22:27). Onkelos translates the word in that verse as dayana (judge). We have an unequivocal verse in Tehillim 75:8 proving that the word means judge, i.e. "ki-elokim shofet zeh yashpil vezeh yarim - For G-d is a judge; He raises up one man while bringing down another." The term elokim for G-d is appropriate at this point as He employed the attribute of Justice when creating the universe.
From a Sod (Kabbalistic) point of view, the word is composed of two separate words kel hem. The first word kel is a name for G-d in the possessive form, the second word hem describing all the other attributes G-d employed when creating the universe. (R. Bachya)