dH stands for degrees of Hardness.
There are two types of hardness. GH and KH.
GH is general hardness. It's the measurement of dissolved calcium and magnesium ions in the water.
KH is the carbonate hardness. It's the measurement of dissolved carbonates in the water. (Calcium Carbonate, Sodium Bicarbonate, etc)
There are test kits that measure both. Typically they work by adding drops into a test sample of specific size until the water turns a specific color. The number of drops equals the dH.