Though I'm not familiar with the Java Iterator, it seems very similar to .NET's IEnumerable.
The advantages of the enumerator/iterator are:
You don't have to know the size of the collection, which in some cases can require N steps to determine, increasing execution time (though it remains technically linear). Instead, you just keep moving to the next element until there aren't any.
Because the cardinality of the collection doesn't have to be known, iterators can allow collections to be generated dynamically, or "streamed" with elements being added while you begin work on what you already have. For instance, you could derive from Iterator and/or overload iterator getters to create classes that generate finite or infinite series "lazily", figuring out what each element in your enumerable collection is when you ask for it instead of when you define the collection. You could also set up a buffered stream, where you process records, packets, etc that you have received, while another thread or process works ahead of you to queue up more for you to work on.
Any collection that can provide an iterator can be traversed in exactly the same way, instead of having to know whether it's indexable, what the method or member is that defines size, etc etc etc. Iterator implementations thus provide an adapter to allow the same code to work on any collection passed to it.
Does Java have an equivalent to .NET extension methods (static methods that are not part of the class definition, but that work on instances of the type and can be called as if they were instance methods)? If so, you can define methods that take an Iterator and produce a result, which could be another Iterator. .NET's Linq library is based heavily on these, providing a very powerful collection-manipulation framework allowing for common operations to be chained together, each operating on the result of the previous operation.
