A hallmark is an official mark or series of marks struck on items made of precious metals — platinum

Platinum

Platinum is a chemical element with the chemical symbol Pt and an atomic number of 78. Its name is derived from the Spanish term platina del Pinto, which is literally translated into "little silver of the Pinto River." It is a dense, malleable, ductile, precious, gray-white transition metal...

, gold

Gold

Gold is a chemical element with the symbol Au and an atomic number of 79. Gold is a dense, soft, shiny, malleable and ductile metal. Pure gold has a bright yellow color and luster traditionally considered attractive, which it maintains without oxidizing in air or water. Chemically, gold is a...

, silver

Silver

Silver is a metallic chemical element with the chemical symbol Ag and atomic number 47. A soft, white, lustrous transition metal, it has the highest electrical conductivity of any element and the highest thermal conductivity of any metal...

 and in some nations, palladium

Palladium

Palladium is a chemical element with the chemical symbol Pd and an atomic number of 46. It is a rare and lustrous silvery-white metal discovered in 1803 by William Hyde Wollaston. He named it after the asteroid Pallas, which was itself named after the epithet of the Greek goddess Athena, acquired...

. In a more general sense, the term hallmark can also be used to refer to any distinguishing characteristic or trait.
Historically, hallmarks were applied by a trusted party: the 'guardians of the craft

Craft

A craft is a branch of a profession that requires some particular kind of skilled work. In historical sense, particularly as pertinent to the Medieval history and earlier, the term is usually applied towards people occupied in small-scale production of goods.-Development from the past until...

' or nowadays by an assay office

Assay office

Assay offices are institutions set up to assay precious metals, in order to protect consumers. Upon successful completion of an assay, Assay offices are institutions set up to assay (test the purity of) precious metals, in order to protect consumers. Upon successful completion of an assay, Assay...

. Hallmarks are a guarantee of certain purity or fineness of the metal as determined by formal metal (assay) testing.
.999 = 24 carat = 99.9%

.916 = 22 carat = 91.6%

.750 = 18 carat = 75%

.585 = 14 carat = 58.5%

.417 = 10 carat = 41.7%

.375 = 9 carat = 37.5%

.333 = 8 carat = 33.3%

24 carat gold is pure gold..
Therefore
.575 or 57.5% = 13.8 carat gold.
Hallmarks are often confused with "trademarks" or "maker's mark".