Example:
var someString = 'hi there';
someString = 'not hi there any more';
The memory occupied by 'hi there' is elligible for garbage collection the second you assign something else to it, namely 'not hi there any more'. Now let's say that you know you're not going to use 'hi there' again, but don't have another handy string to assign to it, you can just 'delete' it.
var someString = 'hi there';
delete someString;
The delete, in this case invalidates the object that 'someString' references, though doesn't necessarily free the memory immediately. This just helps the garbage collector know that you are done with the someString variable, despite the fact that it is still in scope. Perhaps because it was used as initialization for some closure or something like that.
Note: The use of the 'new' keyword does not change the logic above.