Natural selection is a mechanism whereby differences in the phenotypes of individuals cause some of them to survive and reproduce more effectively than others. There is variation among individuals in a population, at least some of which is heritable. Some variants have greater fitness than others, resulting in differential reproductive success. Natural selection accounts for adaptations.
Weismann's experiments determined there was a "barrier" that prevented inheritance of acquired characteristics, and that hereditary information in the germ plasm (genes) contributes to the development of the soma (body), but information never flows in reverse.
The offspring's phenotype is the average of the parental phenotypes, like mixing white paint and black paint to make grey paint. This is incompatible with natural selection.
The view that large mutations were the primary drivers of evolutionary change, leading to sudden changes and the rise of new species ("hopeful monsters").
The reconciliation of Darwinism and Mendelism in the 1930s and 1940s, primarily through the development of population genetics and quantitative genetics, which showed how particulate inheritance can cause continuously varying traits subject to gradual natural selection.
Common descent was widely accepted by scientists soon after On the Origin of Species was published, but natural selection was not widely accepted until the modern synthesis of the 1930s and 1940s.