"The theory of evolution by cumulative natural selection is the only theory we know of that is in principle capable of explaining the existence of organized complexity." -Richard Dawkins
These are bold words. In order for us to assess them for accuracy, we must unpack them, break them into short phrases and study the concepts Dawkins is dealing with.
Theory: Unlike the ordinary usage of this word (a guess), here, the word "theory" means a scientific theory, or a very large, elaborate, abstract model of the universe or one of its aspects used by scientists to guide their investigations and to enable them to make predictions of future findings.
Evolution: A process by which any system gradually changes over time. Biological evolution, which is what we're dealing with here, can be defined as that, when it applies to the history of life.
Cumulative: Changes are retained. They are not temporary innovations. They gradually add up to big changes over time.
Natural Selection: The survival to reproductive age of only a comparatively few offspring produced each generation. The characteristics of the survivors differ in one or more important ways from those who died without issue. Used this way, the word "selection" is understood to be metaphorical for the operations of an unplanned, unguided, natural process.
The only theory we know of: There are no alternatives to the model given that our limited knowledge and experience can offer that could possibly explain a wide variety of observations so concisely and consistently.
That is in principle capable of: The broad fundamentals of the nature of the system under observation are inherently explainable by this theory, but not necessarily every detail of how the system operates.
Explaining the existence: Clarifying. Making plain how something came to be.
Organized complexity: A system consisting of a large number of elements, which are related to one another, forming a coherent, structured whole.
We may now use these concepts to expand upon Dawkins' assertion:
Biological evolution is the very elaborate and abstract model scientists use to describe how living systems change over long periods of time. The version of evolutionary theory we call the Modern Synthesis is built up out of millions of careful measurements and observations made in such fields as genetics, population statistics, cladistics and taxonomy (the study of the classification of organisms through evolutionary ancestry), paleontology, geology, and computer modeling.
Close, patient observation and examination of plants and animals by researchers around the world over many decades helped theorists confirm the existence of biological evolutionary processes.
Natural selection is integral to the structure of evolutionary theory. As noted above, it asserts that a comparatively few successful adaptations are retained each generation while far more unsuccessful ones are lost to death. It further asserts that this process repeats itself down through the generations. This unplanned, unguided, impersonal process gains direction by the accumulation of favorable changes in response to changing conditions in the organisms' environment.
Researchers assert that such things as co-evolutionary predator-prey relationships, known as "biological arms races," and selection of mates based on preferred, visible characteristics, or "sexual arms races," have also created lasting new direction to changing characteristics. As such, they've sped up evolutionary change enormously over that experienced by organisms that reproduced by merely dividing in two.
Consider how many factors go into the survival of one organism. If it's a plant, as a seedling it must land in fertile soil, grow in favorable weather, avoid being eaten by herbivores, and then successfully pass on its favorable traits by producing its own seedlings, sending them into the environment by the means determined by instructions embedded in its genes.
If it's an animal, it must grow and develop normally, avoid deadly diseases, get enough to eat and drink, avoid being eaten by predators, and successfully mate and produce offspring in order for its successful traits to be passed on.
Every one of these factors is subject to the pressures of natural selection.
Biological evolution may be better understood if you considered it as the story of the evolution of the organism's extended family, its long line of descent. That line of descent evolves as members obtain successful adaptations through mutations or sex crossover. As sex cells are produced during meiosis, parts of the chromosomes will break apart and rejoin with others in different configurations than those displayed by the parent's chromosomes.
The individual organism never evolves. Neither does the species as a whole. The successful extended family evolves, and may eventually supplant the entire species. Or it may speciate, separating from the original species to form its own species.
But why, as I said, is biological evolution the best explanation we can come up with at this time considering our all too, too limiting limits as human beings? We are restricted in our investigations of billions of years of evolutionary history to one tiny sliver of the immensity of Earth's history - our own short life spans. We are restricted by the nature of how the bodies of organisms become fossilized. Most organisms never are. We are restricted to the comparatively limited finds made by geologists and paleontologists. Most fossils are never found.
We are also restricted by our current comparatively low level of technological capacity to investigate precisely how our genes retain information on our characteristics and how they express that information in our bodies in the form of proteins. Such knowledge would bring about profound advances in our understanding of the operation of biological evolution when we achieve it, whenever that might be.
Even so, biological evolution is our best explanation for the observed diversity of life because it makes use of the large body of knowledge we do have on hand on the history of life and its present-day characteristics. The theory of evolution is sound because it explains how it all fits together.
It makes plain how single-cell life forms work together to make up multi-cellular life, how the bewildering variety of life on Earth today branched apart over the eons out of earlier common ancestors, and how life has developed large, complex ecosystems in which many and varied organisms relate to one another and form a coherent, structural whole.
Cutting edge research is now being done on the question of the origin of life. This work includes study of how amino acids are built up by chemical reactions, how lipids form, how primitive cells may have formed, and how catalytic reactions may have led complex non-living systems step by step to the emergence of primitive, reproducing, metabolizing, living systems.
Another field of great promise uses genetics by comparing the genomes from species to species. As genotyping of thousands of species proceeds apace, the results are now being used as a kind of DNA clock to determine when major branchings of life occurred, not only comparatively recent speciation events, but very ancient speciations that led to the development of genus, families, orders, phyla and kingdoms, a hierarchical order of descent reflected by the classification system developed by Linnaeus some 270 years ago.
The theory of evolution is a bone of contention for religious people who believe God made us and everything else in nature. Creationists who object to the possibility of the existence of unplanned systems of growing complexity, such as biological evolution, by citing the Second Law of Thermodynamics and its assurance that all orderly systems break down over time, ignore the fact that the Second Law only applies to closed systems.
Bear in mind that that law was developed by scientists in the age of steam to help them understand the workings of heat engines. Steam engines worked by using the difference between hot and cold water to drive pistons, which drove the machinery of the Industrial Revolution. As the temperature difference narrowed while the engine worked, the entropy of the system increased.
Earth is not a closed system. Nor is it a heat engine, at least not in the sense understood in the Industrial Age. It receives its energy from the Sun (mostly in the ultraviolet) and dissipates excess heat into space (mostly in the infrared). This energy flow, along with the fact that Earth is in the Sun's "water zone," (not too hot or too cold, but just right), is what powers evolutionary processes, permitting life to emerge from non-living chemistry and then to grow, to evolve, and to flourish.
There is a school of thought that suggests that the emergence and evolution of life on a planet like Earth, is very likely, even almost a certainty. Unlike those who calculate enormous odds against the uncommanded appearance of such complex things as eyes, blood, and the human brain, these evolutionists insist that the biological imperative of natural selection combines chance and necessity into an unparalleled profusion of natural creativity. Our existence is prima facie evidence for the existence of that creativity.
Evolutionary theory is perhaps at once the most contentious and the most fruitful scientific theory ever developed by modern science. I expect it to continue to grow, evolve, and flourish in the centuries to come.