A Genetic Algorithm (GA) is an optimization method motivated by natural selection and genetics. Parameters of the problem are encoded into a finite length string utilizing a user-defined alphabet (a common approach is to use binary). Once the problem is encoded, the solution begins with a population of solutions (sometimes just random numbers). The GA moves from one generation to the next by evaluating the fitness of each member of the population (i.e., how well it solves the initial problem), selecting the members to parent the next generation (based on fitness) then creating the next generation of solutions.
A good reference on GAs is by David Goldberg.