Three Sides of the Same Multidimensional Coin
Capitalism, science, and evolution, are all the same basic approach to problem solving. They each involve trial-and-error, with a selection pressure “distilling” the good solutions from the bad.
Capitalism works by having businesses compete for business. Businesses produce products for consumers to consume (tautological right?). In the idealized version (which doesn't really exist in practice), consumers reward businesses with better products (or services, etc.) and the businesses with the worst products fail, and “die”.
People have new ideas all the time, for new products, new solutions to old problems, improvements on existing solutions, improvements in efficiency, convenience, taste, longevity—whatever it is. (Marketing somewhat confuses this issue, in practice a business with a superior product can lose to a business with an inferior product simply due to better marketing (or really lots of other reasons too).)
Science works by having scientists compete for explaining things. Scientists produce hypotheses, to explain observed phenomena—the motion of the planets, the origin of the diversity of life, the nature of matter. Ideally these hypotheses are tested against observations, sometimes observations of nature, sometimes deliberate experiments. Hypotheses that withstand the scrutiny of observations develop into theories, and the ones that don't are discarded. As is the case with capitalism, this is the idealized version, the real world introduces a number of complicating factors that can interfere with the ideal execution of this process. Scientists are human, and are prone to suffering a variety of cognitive biases that can interfere with giving a hypothesis a “fair shake”. There can be many other pressures that can distort the process away from the ideal, like universities pressuring researchers to publish, or pharmaceutical companies pressuring their researchers to bring a product to market.
Evolution is nothing other than the fact that organisms produce offspring that aren't exactly like themselves. (Okay it's a lot more than that but I'm trying to keep all this as simple as is possible without losing the point.) Each new individual is a slight variation of it's parent(s), and variations that make the individual more likely to survive to reproduction are (again, tautological!) passed on to the next generation, variations that make the individual less likely to survive to reproduction are less likely to be passed on (duh). Over a very large number of generations these small variations really start to add up, and two populations of a kind of creature that are separated (e.g. by geography) will start develop differences between them. Both may be under the same selection pressures, but the variations generation to generation will be random, so they will likely “find” different solutions to the same problems. This is the nature of speciation.
Natural selection is just one kind of selection, sexual selection occurs when the organisms are influenced by the looks (or behavior, or other characteristics I suppose?) of potential mates. Charles Darwin struggled with the peacock's extravagant feathers—how could such unwieldy feathers improve the likelihood of survival for a peacock? Then he realized the solution: peahens prefer peacocks with extravagant feathers! (We think this is why the males of so many species of bird are so flashy, though I suspect another reason might be that the males can use their flashiness to more easily grab the attention of predators and draw them away from their nests, providing some protection for their offspring. This might be solid science I don't know, seems unlikely I would be the first to think of it.)
None of these ideas are very complicated. They all involve competition, they all involve trial-and-error and failure, and rewards for success. With less “fit” organisms/hypotheses/businesses “dying out” and more “fit” ones thriving.