The word 'evolution' is used with a broad range of meanings, which explains—at least, in part—why there is such a lot of confusion about whether evoultion is a fact or a theory.
The word has its origin in Latin evolutio, meaning "to unroll," such as opening a scroll to the desired column of text. In usage it imples no more than unpacking what is already present in a compact form. According to the Oxford English Dictionary, the term "evolution" was first introduced into a biological context when, in 1670 an anonymous author used it in a review of the embryology of the Dutch entomologist Jan Swammerdam.
Swannerdam held a preformationist view that the egg was essentially an adult with all the parts already nascent and that it needed only the stimulation of the sperm for it to "unroll" or "evolve" into the adult form. Swammerdam used the term "evolution" to describe this change that insects (he was a student of insects) underwent in their development from eggs to adults.
As better equipments, especially of the microscope, enabled better observations, embryologists began to detect in the development of the embryos a series of more primitive forms, as if the process was recapitulating the order of the ancestral species from which they were descended. The term "evolution" shifted from describing the unfolding of the preformed embryo to this describing this recapitulation of the ancestral forms. Later still, as the question of the meaning of the species arose, the term was shifted again to describe the process by which one species, genus, etc, develop from another.
In the discussion about "evolution," it is almost always assumed that everyone knows what the word means and the term is, therefore, almost never defined in any discussion. But the term has broadened so much in its meanings that it is important to be clear what exactly is being intended when the word is used. Those who identify themselves, broadly, as evolutionists are particularly guilty of this, just as they are guilty of putting all Christians into a species called "Creationists" without bordering to recognize, far less acknowledge, that Christians constitute an entire genus.
First, almost any kind of biological changes in a species is said to be proof of evolution having taken place. This can be clearly seen in two classic examples.
In 1955, H. B. D. Kettlewell published an essay, "Selection Experiments on Industrial Melanism in the Lepidoptera," in the journal, Heredity, in which he described what happened to the peppered moth, Biston betularia when conditions changed. The experiment was carried out in industrial Birmingham, England. The moth existed in two forms, a light and a melanic (dark) form. In the unpolluted countryside where the trees were covered with lichen, the light form escaped predation more easily since the melanic form stood out against the lichen and are more easily taken. As a result, the population of the light form increased. When introduced into the polluted city where the trees were covered with soot, the light ones stood out and fell victim to predation while the melanic form got protected by blending more effectively against the soot-covered trees. Here the population of the melanic form increased and the light fell. If the conditions persisted, it was argued, the more adaptive form would increase in number and a new species would eventually evolve.
The Kettlewell experiment was the classic proof of evolution cited in every textbook in the 1960-70s. The logic of the arguments may have been spurious but it was not until the mid-1980's before the example was quietly removed from textbooks (but since everyone was into the game, there was never felt any need for an apology or acknowledgement of the booboo).