To radicalize someone is to shift a person or group's opinions toward either end of the political spectrum. The word comes up a lot during times of political upheaval or revolution when people’s opinions stray far from the mainstream.
To radicalize people is to cause a shift in their beliefs that make them want to take action for social reform. Once they’re radicalized, they'll want big political or social changes and work to make them happen. Personal experience is often radicalizing — sexism, racism, poverty, and perceived injustices radicalize many people to try to change the world. The word can have a darker meaning when radicalization leads to politically motivated violence.