For a population to be in Hardy-Weinberg equilibrium, certain conditions must be met, one of which is the absence of mutations. Mutations introduce new alleles into a population, altering allele frequencies and disrupting genetic stability. By ensuring no mutations occur, the genetic makeup remains constant over generations, allowing for the mathematical predictions of allele frequencies to hold true. Other conditions include a large population size, no migration, and random mating, all of which help maintain genetic equilibrium.