Evolution can occur due to three different phenomena:

Selection is the process by which those alleles (copies of genes) more able to replicate themselves into subsequent generations by doing so become more common. So, for instance, if you have an allele that makes you more resistant to illness, you are less likely to die of disease before reproducing, and so you will be more likely to replicate yourself (and your alleles) into the population, thus making your alleles more common.

Selection can be natural (as in this case) or artificial (it was selectively advantageous in Nazi Germany to have the "race" that they liked, not because of natural forces but because those of "race" that they disliked were more likely to be sent to the extermination camps - the Nazis were imposing artificial selection).

Mutation is the creation of new alleles that had never existed before as a result of alteration of DNA. So, for instance, if one of your gamete-producing cells is struck by a cosmic ray which alters the sequence of nitrogen bases in its DNA, and that cell is the one that is used to conceive your child, then your child will be a mutant, introducing this new allele into the human species. Both of the other mechanisms of evolution must have existing variation in alleles to work upon, and mutation is ultimately the only source.

Drift is where events that happen as a result of chance cause some alleles to become more common or rarer. So, for example, if you are struck by a meteorite and killed, the alleles you carry will become rarer in the human population as a result of your removal from it.

Large-scale evolution, such as the evolution of new species (as opposed to new genotypes), is ultimately this small-scale evolution compounded upon itself. Nonetheless evolution can happen very rapidly under strong enough circumstances.

I am not a biologist but this is an interesting "meta question" that I want to comment on, not necessarily answer. Evolution takes place, and as a result of evolution, we have evolved to the stage where we are able to ask questions such as "What causes evolution?" From the viewpoint of philosophy, we cannot, being a part of evolution, easily ask questions about why evolution happens.

Less philosophically, the driving force for evolution, as for many other natural processes, is the tendency towards increasing entropy in the universe. This tendency can lead to non-equilibrium steady states such as human life forms.

I am sorry but I have made no attempt to simplify this discussion. I hope only to indicate that you have posed a very complex question.

Evolution is the process of genetic change from one generation to the next and may be caused by several methods.

In essence, evolution occurs when some individuals or some alleles (gene types) reproduce themselves more than others, increasing their prevalence in subsequent generations. At the same time, other alleles reproduce themselves less, and become less prevalent in subsequent generations. Therefore, the relative frequency, or abundance of different alleles in a population changes over time and across generations due to this differential reproductive success of different alleles.

First, changes from one generation to the next may be completely random, due to good or bad circumstances experienced by chance by different individuals with different genotypes (genetic make-up). One genotype may be mostly wiped out by a natural disaster due to sheer bad luck, while the other may experience favorable conditions and be able to reproduce due to good luck. In the next generation, therefore, the one genotype that reproduced will be more prevalent.

Another random way that evolution can occur is when individuals mate and alleles are lost or gene frequencies change by random chance. Since only half of all alleles (gene types) in a population are transmitted to the next generation by each mating (i.e., zygotes -- sperm and eggs -- only contain half of their parents' alleles), there is a good chance, especially in small populations,hat certain alleles will be lost or will change in their frequency in the next generation. This type of evolution is called "genetic drift" or "neutral selection" and is more important for smaller populations.

Large populations tend to be more genetically stable and are statistically buffered against variation in genotypes due to these random chance events.

Another way that evolution occurs is by "Natural selection", which is caused by differential survival and reproductive success. Evolution by natural selection occurs when
1) there is diversity among individuals in their characteristics (or traits),
2) certain individuals are better able to survive and reproduce than others because their traits, and
3) these traits are heritable and can be passed onto the next generation through reproduction. By surviving and reproducing, we are able to pass onto the next generation genes and other heritable characteristics of our selves. Those that do not survive and reproduce cannot pass on their traits to the next generation. Therefore, if a population of individuals has a mixture of traits in one generation, but some of these traits cannot survive and reproduce while others can, then the mixture of traits will likely be very different in the next generation due to this differential reproductive success.

A third way that evolution occurs is by mutation, or random changes in alleles outside of reproduction. When these allele changes occur, most of the time they are thought to be harmful and individuals with these mutations are eliminated from the population by either not being able to survive or not being able to reproduce (this is called "negative selection"). However, occasionally,a mutation is beneficial and the mutated individual (or allele) has better survival and reproductive success than others and therefore becomes more common in the next generation (this is called "positive selection").

A fourth way that evolution occurs is a relatively ignored theory called "endosymbioses". This is the idea that certain species arose when they formed very close symbiotic relationships with other species and incorporated the genome (DNA) of both species into one functioning body. Organisms with their own genomes can perhaps sometimes combine with other independent organisms, become dependent upon one another through a close mutually beneficial relationship called "symbioses", and form a whole new organism or species.

One line of evidence for this theory is that mitochondria and chloroplasts have their own DNA and double-layered membranes and closely resemble many ancient prokaryotes (e.g., bacteria). One scientist, Lynn Margulis, proposed that some primitive amoeboid eukaryotes engulfed mitochondria and chloroplasts and learned to incorporate them into their own cellular body rather than digesting them. The eukaryote developed a symbiotic relationship with the mitochondria and chloroplasts, allowing it to efficiently photosynthesize and produce ATP using the Krebs cycle and electron-transport chain. This energy efficiency and ability to photosynthesize was a huge benefit to its survival and reproduction and it was able to pass these mitochondria and chloroplasts onto its offspring.