Evolution is difficult to observe because it usually takes many years to happen. This is one reason why the theory of evolution is still a theory, not a law. Since no-one was around millions of years ago to make observations, take notes and carry out experiments, evolution cannot be proved in the usual scientific sense. However, rapid changes in species have been observed that support the theory.
Before the industrial revolution in Britain, most peppered moths were of the pale variety. This meant that they were camouflaged against the pale birch trees that they rest on. Moths with a mutant black colouring were easily spotted and eaten by birds. This gave the white variety an advantage, and they were more likely to survive to reproduce.
Airborne pollution in industrial areas blackened the birch tree bark with soot. This meant that the mutant black moths were now camouflaged, while the white variety became more vulnerable to predators. This gave the black variety an advantage, and they were more likely to survive and reproduce. Over time, the black peppered moths became far more numerous in urban areas than the pale variety.