It has to do with the Masonic order. The eye is the all seeing eye. It has to do with making a country that is different from any that had been developed before.

What do the symbols on the U.S. $ 1 bill mean?

The Great Seal of the United States appears on the backside of the United States $ 1 bill. The reverse of the seal appears on the left, and the obverse side of the seal appears on the right.

The Continental Congress decided to create a national seal or emblem on July 4, 1776, the same day that the congress adopted the Declaration of Independence. The congress appointed Benjamin Franklin, Thomas Jefferson and John Adams to a committee to come up a national seal. It took six years, three committees, several artistic contributions and many revisions before the final seal was adopted on June 20, 1782.

Since that time, the Great Seal has undergone changes in design, reflecting the tastes and ideas of later generations, but the features of the original design were kept intact. These features are meant to graphically represent the tenets of the new nation.

The unfinished pyramid and the eye in a triangle on the reverse side are classic symbols. The Egyptian pyramid is a symbol of strength and duration; the 13 steps indicate the original number of U.S. states; and the 13 steps leading to an unfinished summit indicates future growth of the nation. The eye is known as the “Eye of Providence” and is surrounded by rays of light. According to Webster’s New World College Dictionary, “providence” can mean:

a looking to, or preparation for, the future; provision.
skill or wisdom in management; prudence.
a) the care or benevolent guidance of God or nature, b) an instance of this.
God, as the guiding power of the universe.
The single eye shows up in Egyptian mythology as the Eye of Horus, an ancient god of the Egyptians. The eye represented wisdom, health and prosperity. Some people think that the “all-seeing eye” is a symbol of Freemasonry, a fraternal organization, and they interpret this as proof that the Founding Fathers believed in Masonic principles and wanted to impose Masonic order on the United States. This essay addresses that rumor.
Here are the other symbols on the Great Seal.

The obverse side:

The 1782 secretary of Congress, Charles Thomson, adopted the bald eagle as the prominent feature of the design.
The shield, or escutcheon, is shown on the breast of the eagle without any support, indicating the self-reliance of the United States. Thirteen red and white stripes appear on the shield, signifying the 13 original states. The red color represents hardiness and valor, and the white represents purity and innocence. These stripes support and unite with the top blue band, which represents Congress. Blue signifies vigilance, perseverance and justice.
The eagle’s talons hold 13 arrows in the right and an olive branch in the left. These symbolize the power of war and peace, respectively. The number of arrows represents the 13 original states.
The constellation of 13 stars (states) above the eagle’s head signifies the United States’ rank among other sovereign powers.
The motto, “E Pluribus Unum,” written on the banner held in the eagle’s beak, is Latin meaning “Out of many, one,” conveying the union of the States.
The reverse side:
The pyramid
The eye in the triangle above the pyramid
The Roman numerals, MDCCLXXVI, appear on the base of the pyramid and translate to 1776, the year of independence.
Above the “eye” are the Latin words “Annuit Coeptis.” This translates to “He has favored our undertakings.” This line is associated with the “Eye of Providence.”
Below the pyramid are the Latin words “Novus Ordo Seclorum,” meaning “A new order of the ages,” referring to the birth of America in 1776.
In 1935, the Department of Treasury proposed the use of the obverse and reverse sides of the Great Seal on the back of the $ 1 bill, originally with the obverse on the left hand side and the reverse on the right. Before approving the design, President Franklin Roosevelt decided to switch the order of sides of the seal, and then added “The Great Seal” under the reverse and “of the United States” under the obverse.

Edit: I assume you mean the US one dollar bill as we in Australia haven’t had a one dollar note for a long time.
It was replaced by the one dollar coin in the mid-eighties. We only have one dollar coins these days.
(It was rarely called a one dollar bill, it was usually called a one dollar note.)

Good one Paul. I was thinking of the Jamaican Dollar.