What is Hardy-Weinberg equilibrium?
In Hardy-Weinberg equilibrium, equilibrium refers to a condition of non-evolution that is the inherent characteristic of populations when:
free of mutation; free of natural selection; the population is infinitely large; all members of the population breed; all mating is totally random; everyone produces the same number of offspring; there is no migration in or out of the population.
In other words, in a population in which one or more of the above restricting conditions is not true and does occur (e.g., migration in or out does indeed occur or mating is not in fact random), evolution will occur and the population will not be in equilibrium with inherent stability demonstrated and evolution not occurring.
Hardy-Weinberg equilibrium equation identifies the genotype frequencies in a population and tracks frequency changes from one generation to the next. When considering dominant and recessive genes, frequency is the change in ratio between dominant (B) and recessive (b) traits, so that if the parent generation has 91% B frequency and 9% b frequency while the next generation has 88% B frequency and 12% b frequency, then there has been a change in gene type frequency (i.e., frequency of occurrence) and a corresponding occurrence of evolution. The Hardy-Weinberg equilibrium equation identifies probable frequencies in a gene pool and tracks frequency changes.
The great significance is that before Hardy's and Weinberg's work, the assumption was that dominant genes would in time overpower or cancel out recessive genes in a process called "gene eating," however Hardy and Weinberg proved that dominant genes can equally easily decrease in frequency in a gene pool of a large population.
[for more detail, see Hardy-Weinberg Equilibrium Model, Dr. Dennis O'Neil, Palomar College.]