Spring Boot is a Spring module that aims to simplify the use of the Spring framework for Java development. It is used to create stand-alone Spring-based applications that you can just run. So, it basically removes a lot of configurations and dependencies. Aiming at the Rapid Application Development, Spring Boot framework comes with the auto-dependency resolution, embedded HTTP servers, auto-configuration, management endpoints, and Spring Boot CLI.
So, if you ask me why should anybody use Spring Boot, then I would say, Spring Boot not only improves productivity but also provides a lot of conveniences to write your own business logic.