The aim of the Maybe type is to avoid using 'null' references.
A Maybe<T> represents a possibly non-existent value of type T.  The Maybe
type makes it impossible (without deliberate effort to circumvent the API)
to use the value when it does not exist.
A Maybe<T> is either unknown(), in which case a known value does not exist,
or definitely(v), in which case the value is known to be v.
A Maybe<T> is iterable, which means you can use it with the for statement
to extract a value and do something with it only if there is a value.
   class Customer {
       public Maybe<String> emailAddress() { ... }
       ...
   }
   for (String emailAddress : aCustomer.emailAddress()) {
       sendEmailTo(emailAddress);
   }
Maybe<T> being iterable really comes into its own when combined with the Guava
(previously google-collections) library, which has useful functions for
working with iterables. You can then work in terms of entire collections
of things that might or might not exist, without having to test for the existence
of each one.
For example, if I have a collection of 'maybe' email addresses, some
of which might exist and some might not:
    Iterable<Maybe<String>> maybeEmailAddresses = ...
I can get a set of only the actual email addresses in a single expression:
    Set<String> actualEmailAddresses = newHashSet(concat(maybeEmailAddresses));
The newHashSet and concat functions are defined by Guava.  Concat
creates an Iterable<T> from an Iterable<Iterable<T>>, concatenating
the elements of each sequence into a single sequence.  Because
unknown() is an empty iterable, the concatenated iterable only returns
the definite values.
More likely, I have an iterable collection of Customers.  Using a
Function, I can write a single expression to get the email addresses
of all customers who have an email address:
Here's a function to map a customer to its 'maybe' email address:
   Function<Customer,Maybe<String>> toEmailAddress = new Function<Customer, Maybe<String>>() {
       public Maybe<String> apply(Customer c) { return c.emailAddress(); }
   };
And here's how to use it to get all the email addresses that my
customers have, so I can send them product announcements:
   Set<String> emailAddresses = newHashSet(
               concat(transform(customers, toEmailAddress)));
If I just want to send emails, I don't need the hash set:
   for (String emailAddress : concat(transform(customers, toEmailAddress))) {
       sendEmailTo(emailAddress);
   }
The name "concat" is a bit obscure, so I'd probably define an alias
named, for example, "definite", to make the code more readable at the
point of use.  And the Function definition is a bit clunky, but Java
doesn't have (and doesn't look likely to get) a clean syntax for
referring to existing functions.
That's not to say that Maybe doesn't have useful methods to work with
individual instances.  For example, the otherwise method:
   T otherwise(T defaultValue);
will return the Maybe's value if it is known and the defaultValue if it is not.
E.g.
       assertThat(unknown().otherwise(""), equalTo(""));
       assertThat(definitely("foo").otherwise(""), equalTo("foo"));
Otherwise is overloaded to take a Maybe<T> as a default:
   Maybe<T> otherwise(Maybe<T> maybeDefaultValue);
which lets you chain otherwise expressions:
   assertThat(unknown().otherwise(definitely("X")).otherwise(""), equalTo("X"));
Maybe also has a method that uses a function to map a Maybe<T> to a Maybe<U>
    <U> Maybe<U> to(Function<T,U> mapping);
which would transform unknown() to unknown(), otherwise apply the function to
the definite value and return the result wrapped in a Maybe.
Similarly there is a query method that takes a Predicate<T> and maps a Maybe<T>
to a Maybe<Boolean>.
All of which API calls make it impossible (without deliberate effort) to try to
get the value of nothing.