We are just an advanced breed of monkeys on a minor planet of a very average star. But we can understand the Universe. That makes us something very special.
With this statement, Hawking both minimizes and embellishes the importance of the human in the greater scheme of things. We are little more than monkeys from an evolutionary standpoint - human DNA and monkey DNA are only a couple of markers apart. Our home, Earth, is not particularly large, nor does it have any influence over the other planets in our solar system. Even the star Earth orbits is pretty non-remarkable. All in all, humans are a mediocre lot with no great elements of wonder about them - except, we have the ability to understand the Universe. As Hawking explains in his book, this understanding was a long time coming. Many different scientists, philosophers and astronomers posited many different theories about the way in which the Universe worked - until the secret was unlocked, and now, this information is available for every human on this little planet to understand. That makes humankind special, because understanding the Universe is the key to understanding how everything has come into being since the beginning of time.
Any physical theory is always provisional, in the sense that it is only a hypothesis. You can never prove it. No matter how many times the results of experiments agree with some theory you can never be sure that the next time the result will not contradict the theory.
In many ways, this statement suggests that all scientific experiments succeed based on a law of averages rather than as proof that a theory is correct in the way that it has been interpreted. Theories are always going to be just that; they can never be incontrovertible evidence because even though an experiment might prove the same theory hundreds of times, who can say with complete certainty that they will continue to do so? The nine hundred and first time an experiment is undertaken there is a possibility that it might indeed disprove a theory, and continue to do so for another thousand times. Because of this, there is no way that a theory can ever be proved beyond a doubt; even the most reliable science cannot turn the more sound theory into a fact.