“A cut above” dates from the eighteenth century and literally means the quality of the cutting or fashioning of a person’s clothing.
The superior appearance or station in life of someone with a good tailor or milliner is obvious when compared with a common man or woman, making them a “cut above” the ordinary.
The phrase is related to the nautical phrase “The cut of her jib,” meaning the style or cut of a ship’s sails.
You can also be a “cut below,” as in “The girl herself is a cut below par” (A.B. Walford, 1891).