Looking through the code, the author states:

From _initialize (called from new):

#                Caches the first value of the iterator in %next_value
+_for.
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and value:

    # Notes:         Keeps one forward-looking value for the iterator 
+in
    #                   %next_value_for.  This is so we have something
+ to
    #                   return when user's code throws Am_Now_Exhauste
+d.
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Assuming this is to know when the iterator will be exhausted, as pKai said.

For your second example, this is explicitly stated in the docs:

When you use an iterator in separate parts of your program, or as an a
+rgument to the various iterator functions, you do not get a copy of t
+he iterator's stream of values.

In other words, if you grab a value from an iterator, then some other 
+part of the program grabs a value from the same iterator, you will be
+ getting different values.

This can be confusing if you're not expecting it. For example:

    my $it_one = Iterator->new ({something});
    my $it_two = some_iterator_transformation $it_one;
    my $value  = $it_two->value();
    my $whoops = $it_one->value;
Here, some_iterator_transformation takes an iterator as an argument, a
+nd returns an iterator as a result. When a value is fetched from $it_
+two, it internally grabs a value from $it_one (and presumably transfo
+rms it somehow). If you then grab a value from $it_one, you'll get it
+s second value (or third, or whatever, depending on how many values $
+it_two grabbed), not the first.
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IMO, if you needed to use the value returned from the iterator, save it somewhere instead of using a variable in the same scope - although I realize that your code is more than likely a simplification of what you're really trying to do