In an attempt to answer the question as asked, an SDK is a Software Development Kit. It is a collection of tools, libraries, api's, source code, licenses, examples, documentation, and/or anything else required to develop software applications in a specific programming language or framework.
The integration of an SDK into an IDE is essentially the ability for an external application to leverage the capability provided by the SDK, and make programming and application writing easier for the user.
The SDK configured in an IDE might provide the capability for the IDE to allow API auto-complete, object inspection, source code compile/debugging, syntax highlighting, integrated code inspection and warning/error information, just-in-time compiling, unit testing, etc.
An SDK (such as Java) can be very big, containing a lot of information and capability. Other SDK's may simply be a set of API's or libraries, and as such, may not be as conducive to being used with an IDE, and could be deemed as "convenient" from the perspective of a user that is not familiar with the concept of an SDK in the "Java" sense.
The IDE's capability to leverage what is provided by the SDK may be determined by a couple things: 1. The SDK doesn't provide a very comprehensive set of tools and capabilities that allow an IDE to do what it does best, and thus appear "useless" 2. The IDE just didn't implement the SDK capability all that well
Hopefully this provides some insight...