You wouldn't normally use Double, Integer, etc. (Occasionally Integer etc. can be useful to store an 'optional' value - you might want it to be null sometimes. This is less likely with Double because NaN is available for those.)

The reason Double exists is as follows. Java has two main types of value: objects (essentially like C/C++ pointers without the arithmetic), and primitive values (e.g. double). Classes like ArrayList can be defined to accept any Object, which allows users to store String, File or whatever they like in one - but primitive values like double are not covered by such a definition. So classes like Double exist to make it easier for classes like ArrayList to store doubles, without requiring the authors of ArrayList to create special versions for all the primitive types.

It is called AutoBoxing

Autoboxing and Auto-Unboxing of Primitive Types Converting between primitive types, like int, boolean, and their equivalent Object-based counterparts like Integer and Boolean, can require unnecessary amounts of extra coding, especially if the conversion is only needed for a method call to the Collections API, for example.

The autoboxing and auto-unboxing of Java primitives produces code that is more concise and easier to follow. In the next example an int is being stored and then retrieved from an ArrayList. The 5.0 version leaves the conversion required to transition to an Integer and back to the compiler.

Before

ArrayList<Integer> list = new ArrayList<Integer>();
  list.add(0, new Integer(42)); 
  int total = (list.get(0)).intValue();

After

ArrayList<Integer> list = new ArrayList<Integer>();
  list.add(0, 42);
  int total = list.get(0);

Yes, comparing a Double to a double in this way is just fine. This is because Java automatically converts the Double to a double anyway through auto-unboxing.