The discovery of the process of biological evolution is arguably mankind's single greatest discovery because it marked the departure from explanations about our origin based on religion and myth to explanations based on objective reasoning and empirical evidence.
Of course, the notion of biological evolution did not just instantly appear when Charles Darwin wrote his Origin of Species in 1849. Before then other thinkers were aware that things that existed in nature were probably part of a grand progression of change over time. People saw that there were changes to the physical features of the earth that must have occurred over immensely long periods of time - millions of years - as contrasted with the older idea that everything was created instantly by a Supreme Being.
Further, the presence of the fossilized remains of long dead species and the observance of progressive development of those species in the fossil record at first fueled and then solidified the idea that the form of animals actually evolved over time.
When Darwin arrived on the scene of scholarly discourse with the publication of his book everything changed because what he did was show evidence of evolution and an explanation for why it occurred.
Darwin formulated a scientific argument that commenced with the publication of his book and continues to this day. It is an argument for a theory of "natural selection" that has now become so replete with consistent verifiable deductions based upon observable nature that there is no doubt based on reason of its validity.
Darwin's proposition, that the changing conditions of life on earth has allowed for the propagation of a given species due to certain inheritable characteristics of members of that species that make such individuals more survivable during such changes and thus able to reproduce, is a testable theory based on observable phenomena.
Darwin pointed to the observable features of embryological development whereby related species exhibit similar anatomical structures as embryos that are not carried forward in the adult version - such as gill pouches in all vertebrate embryos including humans - as evidence of a common aquatic ancestor for all vertebrates.
Vestigial characteristics - our tailbone for example - is a structure of our anatomy that is of no use to us but can be explained as something inherited from our ancestors who must have had a use for it. There are many examples - such as blind cavefish that retain empty eye sockets or flightless birds that retain useless underdeveloped wings.
Similar species have anatomical structures that are similar but are used for different purposes. For example the forelimbs of all mammals - dogs, bats, people have the same bones but they are used for different purposes. This points to a common ancestry for these very different species.
Darwin's answer to the question "Why does evolution occur?" is simple and straightforward. Evolution occurs because physical conditions on the earth change. When any slight chance modification in the make-up of a member of a species favors that member in coping with the change in its environment that member is more apt to survive and propagate. Over time those members possessing the favorable trait will outnumber those without it such that eventually all members of the species will possess the favorable trait. The overall phenomenon can thus rightly be described as the evolution of the trait by natural selection.
Darwin's theory as espoused in his writings was a breath of fresh air that swept away stultifying modes of thought anchored in religious dogma. He pointed the way to an intellectually honest inquiry into the history of not only plants and the lower animals but of man himself and his true place in the scheme of life on this planet.