Nondimensionalization is the transformation of an equation to an equivalent equation, eliminating some or all the variables that have units (e.g., seconds, meters, kilograms, etc.). This may be to simplify the equation and/or to make apparent the modeled phenomenon's intrinsic characteristics. In place of the variables with units may be variables with ratios.
Such a ratio may be between values in the original equation that have similar units, but the equation may need to be recast first so as to provide two such values. If such a means is not evident, a quantity may be chosen to form such a ratio, e.g., one that has a natural significance, but other times, a seemingly-arbitrary quantity is chosen and the "nondimensionalization" seems little more than merely adopting new units. For example, expressing a speed as a ratio with c might make the physics more evident, while expressing it as a ratio with "1000 meters per second" seems to be little more than changing to a more convenient unit.