First Water means "highest quality" and is a term which originates from the gemstone

Gemstone

A gemstone or gem is a piece of mineral, which, in cut and polished form, is used to make jewelry or other adornments...

 trade. The clarity of diamond

Diamond

In mineralogy, diamond is an allotrope of carbon, where the carbon atoms are arranged in a variation of the face-centered cubic crystal structure called a diamond lattice. Diamond is less stable than graphite, but the conversion rate from diamond to graphite is negligible at ambient conditions...

s is assessed by their translucence; the more like water

Water

Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

, the higher the quality. This comparison of diamonds with water dates back to at least the early 17th century, and Shakespeare alludes to it in Timon of Athens

Timon of Athens

The Life of Timon of Athens is a play by William Shakespeare about the fortunes of an Athenian named Timon , generally regarded as one of his most obscure and difficult works...

, 1607. The 1753 edition of Chambers' Encyclopedia has this under an entry for 'Diamond':

"The first water in Diamonds means the greatest purity and perfection of their complexion, which ought to be that of the clearest drop of water. When Diamonds fall short of this perfection, they are said to be of the second or third water, &c. till the stone may be properly called a coloured one."