Hi, to understand their usage, you must know the difference between the two.
As you might know that a nested class is by default a member of its enclosing class. An inner class (or the non-static nested class) can access any of the data members of its enclosing class i.e., even if its declared private, it will be accessible by it. Whereas a static nested class can’t do so, rather it can interact with the instances of its outer class. In other words, a static nested class behaves just like a top-level class. In your example, since your LinkedList. Entry class in not accessing any of the LinkedList members, it is kept as static.
Hope this clears your doubt.