Modernization describes the processes that increase the amount of specialization and differentiation of structure in societies, resulting in the move from an undeveloped society to a developed, technologically driven society. How is the idea of modernization related to social movement and social change?

The question implies a sociological definition whereby a society moves from a traditional agrarian rural society to a progressive, technological, or industrialized urban society. The impetus for the evolution is technological advances reshaping society towards specialization and away from generalization and diversification. The historical evidence from the Renaissance Period, the Industrial Revolution, and more recent Technological Revolution, as well as globalization, are insightful when considering how modernization relates to social movements.
Changes in human interactions, relationships, and organizational structures are an inevitable consequence of modernization. Possibly an overgeneralization, social movements, and social change are the responses to modernization. Globalization is an example. In some instances, societies have embraced globalization and mitigated the social consequences by liberalizing social programs to protect citizens during the transitional period from an agrarian to industrialization and developing technological society. In other instances, some communities have hunkered down, vehemently protested, and resisted change.
In either case, social movements are inextricably linked to the pro or con modernization of society. Within this context is the notion of specialization or the idea a person needs to become an expert in one particular skill to survive and succeed in a technologically advanced society.
In a world driven by technological advance, the idea is a person will have to develop skills that align with the needs of the technological change. In past times, generalization or a person with knowledge in multiple skillsets was coveted. Modernization does not entirely eliminate the need for generalists, but it significantly devalues their need in terms of economic and societal worth. We consider an educator critical to a functioning society, but by many measures, an engineer is more highly valued, even though without education, an engineer would not have the skills to perform their specialty.
By nature, a person engaged in generalization is not restricted to one skillset and interacts with a broader, more diverse group. Specialization is the idea of expertise in one skillset and interacts with a much less diverse group. A person engaged in a specialty limits their interaction to people with the same interest. For example, an engineer designing a bridge would have no need to interact with the construction worker pouring the cement to construct the bridge. Specialization is an isolating factor in society.
To tie this all together, the prevailing idea is that modernization requires a high degree of people with specialized skills. Specialization reduces the interaction between various levels of society and creates momentum for a response. Social movements are the response to modernization and the inevitable de-emphasis on diversity as both a skill and an essential part of human interaction in society. Social change is either the coerced effect of modernization or the humane consensus that since change is inevitable, then some provision must be made, for those that change will have a negative consequence.
https://hbr.org/2011/07/the-big-idea-the-age-of-hyperspecialization

https://www.snhu.edu/about-us/newsroom/2017/11/what-is-social-change