What theory explain how a new idea or product gains acceptance and spreads through a specific population or subset of an organization?

The correct answer is diffusion of innovation theory.

Explanation:

The DOI or diffusion of innovation theory was postulated in 1962 by E.M. Rogers. It is considered as one of the oldest theories in the field of social science. It was deduced in order to illustrate how with time, a product or an idea attains momentum and spreads via a particular social system or population. The eventual outcome of this diffusion is that the individuals, which are the components of a social system, adopts a novel behavior, notion, or a product.  

Here adoption signifies that an individual does something distinctly than what he or she was doing previously. The prime condition of adoption is that the individual must acquire the behavior, idea, or product as a novel or innovative thing. Getting amended with a novel concept, product, or behavior does not take place instantaneously within a social system, however, it is a thing in which some individuals possess the tendency to adopt a new thing more easily in comparison to others.