Genetic algorithm is a search heuristic. GAs can generate a vast number of possible model solutions and use these to evolve towards an approximation of the best solution of the model. Hereby it mimics evolution in nature.
GA generates a population, the individuals in this population (often called chromosomes) have a given state. Once the population is generated, the state of these individuals is evaluated and graded on their value. The best individuals are then taken and crossed-over – in order to hopefully generate 'better' offspring – to form the new population. In some cases the best individuals in the population are preserved in order to guarantee 'good individuals' in the new generation (this is called elitism).
The GA site by Marek Obitko has a great tutorial for people with no previous knowledge on the subject.
To explain the example I will use my version of the Knapsack problem.
You are going to spend a month in the wilderness. You’re taking a backpack with you, however, the maximum weight it can carry is 20 kilograms. You have a number of survival items available, each with its own number of “survival points”. You’re objective is to maximize the number of survival points.