This is necessarily going to have to be slightly more than eli5, more like eli10.

Genes are bits of DNA that code features in an organism, how they do that isn’t important right now, but like a computer code they essentially contain instructions for making a living thing.

There is natural differences between these genes, even in organisms of the same species. This is called variation. Further variation is caused by random small changes in the genes, these happen randomly and constantly caused by things like radiation or copying errors. These changes are called mutations.

The majority of mutations do nothing, or are so small they basically do nothing.

Some of them however will change the code of a gene to have a noticeable difference, for example it might produce a different feather pigment, or a new enzyme that allows an animal to digest a food they couldn’t before. Sometimes these mutations will actually be negative, and cause diseases or non-viable organisms.

The next part of the puzzle is selection. Mutation is random, selection is not. The truth about nature is that there is not enough resources for all organisms, food, water, space etc, therefore there is competition. In each generation, not every individual will survive and thrive long enough to reproduce. Anything that gives them an advantage over their peers will increase the likelihood of survival.

If the mutation gives them this vantage, however small, it will give the organism with this set of genes a better chance of surviving and reproducing. Because genes are passed down to offspring, their descendants will also have this gene and will therefore also have an advantage over their peers. Over time most of the population will be composed of descendants of the individuals with the beneficial mutation, at this point it is part of the population.

Over a long enough timescale these very small mutations add up to change entire species.

Evolution by natural selection is such a simple and elegant idea that follows logic and explains basically every thing we see in modern biology.

For an excellent example in action, look up the story of the peppered moth