Final answer:
The JavaScript programming statement creates a new instance of a String object, named 'mystring' with the value 'this is a string object'. It is less common to use String objects than string literals, but some specific features might require the instantiation of a String object.
Step-by-step explanation:
The programming statement var mystring = new String('this is a string object') in JavaScript is used to create a new instance of the String object wrapper. The name of the newly created instance of a string object is mystring. The value of the string object is 'this is a string object'.
In JavaScript, strings can be created either by using string literals or by creating String objects with the new keyword. String literals are more commonly used and recommended due to their simplicity and performance benefits. Creating a string object using the new keyword is less common and is generally not recommended unless a specific feature of String objects is required. Typically, such features are rarely needed, and direct string literals serve most purposes.