It makes two new individuals by somehow combining two old ones. There are several variations of crossover. The most simple version is one-point crossover. It works by selecting a point at which the chomosomes are cut off randomly. The parts that are cut off are then switched to make two new chromosomes.
Mutation introduces random changes to chromosomes.
It is a mechanism that has only a small chance of occurring. It simply flips a bit in a chromosome, or if the chromosome is made out of floating point numbers, it changes a number. This simple process is repeated until the entire population is reproduced. The new population is decoded and the fitness of the newly created individuals is calculated. At this point, the process starts all over again.