parseDouble() method is used to initialise a STRING (which should contains some numerical value)....the value it returns is of primitive data type, like int, float, etc.
But valueOf() creates an object of Wrapper class. You have to unwrap it in order to get the double value. It can be compared with a chocolate. The manufacturer wraps the chocolate with some foil or paper to prevent from pollution. The user takes the chocolate, removes and throws the wrapper and eats it.
Observe the following conversion.
int k = 100;
Integer it1 = new Integer(k);
The int data type k is converted into an object, it1 using Integer class. The it1 object can be used in Java programming wherever k is required an object.
The following code can be used to unwrap (getting back int from Integer object) the object it1.
int m = it1.intValue();
System.out.println(m*m); // prints 10000
//intValue() is a method of Integer class that returns an int data type.