Genetic Operators

Genetic variation is a necessity for the process of evolution. Genetic operators used in genetic algorithms are analogous to those which occur in the natural world: survival of the fittest, or selection; asexual or sexual reproduction (crossover, or recombination); and mutation.
Crossover
In genetic algorithms, crossover is a genetic operator used to

Fitness

Fitness is used to determine which chromosomes will be used for the next generation. Mathematically, for chromosome S_k: fitness = f(S_k) where: k = 1,..., n; n is a population size, which function that you use to calculate the fitness is obviously dependant on how you decide to encode the string to represent your problem.