String s = "Test";
Will first look for the String "Test" in the string constant pool. If found s will be made to refer to the found object. If not found, a new String object is created, added to the pool and s is made to refer to the newly created object.
String s = new String("Test");
Will first create a new string object and make s refer to it. Additionally an entry for string "Test" is made in the string constant pool, if its not already there.
So assuming string "Test" is not in the pool, the first declaration will create one object while the second will create two objects.