The Spring that I've used (the DI Framework, Spring Integration, Spring MVC) is mainly designed to simplify and standardize enterprise applications. Mostly this involves standard and automated ways to "wire" together applications. This includes DI, but also includes configuration (e.g. configuration to enable a deployment pipeline), communication between components/services (client and server mapping of messages in a message bus to their ser/de impl and schema definitions, database interfaces), service and UI implementations themselves (SpringMVC, Spring Boot), etc. The benefit is that Spring is a glue layer that integrates all these various pieces of "enterprise" systems with minimal boilerplate.
I don't have much experience with Java EE, so can't comment. My experience with Spring is not very positive--it enables and encourages applications and systems to have complex dependency graphs, and so often I've seen this result in giant balls of mud that, despite Spring's claim that it enables decoupled and modularized design, are rat's nests of unexpected coupling and hard-to-predict behavior.