In a very simple way the equation describes the reaction. NAD is reduced using 2 hydrogen atoms. The two hydrogen atoms can come from one reactant (lactic acid fermentation) or from two (in a reaction of glyceraldehyde-3-phosphate to 1,3-bisphosphoglycerate; as shown in the figure below).
First of all, I will pick a particular example from glycolysis, catalyzed by glyceraldehyde-3-phosphate dehydrogenase.
Phosphate by its own has one hydrogen at cytosolic pH (because of the pKA). Thus in this reaction, there are two hydrogen atoms. One hydrogen atom is in the form of a hydride (a proton and two electrons) from the aldehyde group. This hydrogen atom is used to reduce NAD+ to NADH. A second hydrogen atom (in the form of a proton) comes from the phosphate. In the bisphosphoglycerate form, the proton dissociates from the phosphate group and is in solution.
The eventual fate of the electrons that were used to reduce NAD+ to NADH is the electron transport chain (in the mitochondria). In some cases, though, for example muscle cells in an anaerobic environment, or other species that don't have an electron transport chain, the electrons are used in fermentation of pyruvate to alcohol or lactic acid. When NADH donates its electrons in either case, it is then oxidized back to NAD+.