A genetic algorithm is a stochastic search heuristic, which means its a semi-random search method, that can not easily be predicted. Genetic algorithms are analogous to the process of natural selection seen in nature, with different populatation members having different 'fitness' ratings which impact those members ability to pass on traits (or even thereself) to the next generation. Typically a genetic algorithm implementation consists of a population, which consists of chromosomes, which contain the information which will form the result which the population will be evaluated on. Chromosomes contain, genes which the smaller components of the chromosomes, and will be spliced during crossover if the chromosome is fit enough. The genes are typically expressed as binary values (1 or 0), and these will be interpreted into whatever sort of data the program is searching (in the case of the above demo it interprets the genes as numbers and operators). The population will go through several generations to find a result, which involves rating the fitness of all the population member using some sort of metric and then using that to select and generate members for the new population with the methods of Crossover, Mutation and Elitism.
Selection is the process of deciding which population members get to either contribute their genes, or themselves, to the next generation. A common method for selection is Roulette Selection, which is a method which increases the chance of a high fitness population member without guarenteeing its selection.
Crossover involves taking two chromosomes, and picking a random point on the chromosomes list of genes and create a new chromosome made of one chromosome upto that point, and the other after that point.
Elitism involves the presevation of particularily effective population members from one generation to the next.
Mutation is the process of flipping random bits in the genes of chromosomes. Usually this is very low percentage chance, and is used to introduce change to overly stable populations.