Charles Darwin put forward the theory of evolution by natural selection after a round the world expedition, where he made many observations of living things. He backed these up with years of experiments and discussion, and his thinking was linked to growing knowledge of geology and fossils. The theory developed over time from information gathered by many scientists, not just Darwin.
The theory has three main points. First, individuals within a species show a wide range of variation for a characteristic. Second, the individuals with characteristics best suited to the environment are more likely to survive and breed successfully. Third, the characteristics that helped them survive are passed on to the next generation.
Darwin published his ideas in On the Origin of Species in 1859, and there was a lot of controversy. The theory was only gradually accepted for three reasons. It challenged the idea that God made all the animals and plants on Earth. There was not enough evidence at the time to convince many scientists. And the mechanism of inheritance and variation was not known until 50 years after the theory was published.
Other theories existed too. Jean-Baptiste Lamarck suggested that changes an organism gains during its lifetime can be inherited. We now know that in the vast majority of cases this cannot happen.