Managing cloud infrastructure through the AWS Cloud Development Kit (CDK) allows developers to define their infrastructure using familiar programming languages such as TypeScript, Python, and Java. The CDK provides a high-level object-oriented abstraction over AWS CloudFormation, enabling users to define their infrastructure in code and then automatically deploy it to AWS with ease. This approach to infrastructure as code (IaC) allows for more efficient and scalable management of cloud resources, reduces the risk of manual errors, and facilitates collaboration among team members. By leveraging the CDK, developers can streamline their infrastructure management processes and focus on delivering more value to their customers.