The Hardy-Weinberg Principle states that allele frequencies in a population should remain constant unless one or more factors cause those frequencies to change. This principle is even able to predict, with the use of a Punnett square.

ie)

punnett.gif

Here, E and e both stand for alleles in a gene, with E being the dominant allele while e is the recessive allele. The three genotypes that are a result of this are:
EE, Ee, and ee.

You then use an equation to find out the frequency of the genotypes:

p*p + 2pq + q*q = 1
p + q = 1

where p is the dominant allele and q is the recessive allele


Let's say the frequency of the E (dominant) allele is 30%, or 0.30, and the frequency of the e (recessive) allele is 70%, or 0.70.
We should rearrange the formula to fit our alleles; E*E + 2*E*e + e*e = 1:

so then we have (0.30)(0.30) + 2(0.30)(0.70) + (0.70)(0.70) = 1

The chances of an individual in the next generation having the genotype EE is (0.30)(0.30) = 0.09 or 9%
The chances of an individual in the next generation having the genotype Ee is 2(0.30)(0.70) = 0.42 or 42%
The chances of an individual in the next generation having the genotype ee is (0.70)(0.70) = 0.49 or 49%

If these frequencies occur in a population using this formula, then genetic equilibrium is taking place; if not, evolution is occurring.
There are 5 reasons as to why evolution may take place and disrupt genetic equilibrium in a population:

Nonrandom Mating
Small Population Size
Immigration/Emigration
Mutations
Natural Selection



Significance
The importance of the Hardy-Weinberg Principle is that it allows us to determine if or if not a population is evolving by looking at the genotype frequencies. If it is evolving, species will change over time, including humans, and the organisms around us, changing our lives.