Why have humans evolved much more quickly than other animals?
This question appears to address at least two distinct concepts:

the &quot;speed&quot; of evolution
whether there is some &quot;end goal&quot; that evolution seeks

I will provide an explanation of each separately below:
The Speed of Evolution
The speed at which a species evolves—that is, the speed at which it acquires new heritable characteristics—can be affected by numerous factors. Among the most obvious which come to mind are:

existing population size
reproductive cycle rate
number of offspring
offspring survival rate
environmental demands

That said, have humans evolved faster than other species?
On the whole, I do not feel that I could say without a doubt that humans have evolved significantly faster than other organisms. Considering the above factors (we have a slow reproductive cycle, few offspring, etc.), it seems unlikely but this is where a zoologist would know better. The answer provided by bobthejoe may provide insight as well.
I would just raise a word of caution before leaping to the conclusion that we have evolved rapidly without looking into it, because while we often study human evolution quite extensively in biology classes and thus are more aware of changes like upright walking and opposable thumbs and increased brain size, that doesn't mean other animals didn't evolve that much as well (we just don't learn about them in as much detail). Being a psychologist and not a zoologist, I do not have the knowledge to say with any surety that other species did not evolve in their own ways to the same magnitude as we have in the last 3-4 million years, so perhaps someone else can help you there.
But you ask whether we have a particular part of our brain that no other animal has; the answer to this is no, but the parts of our brains which we do share with animals are often much larger than as seen in those other species.
The &quot;Goal&quot; of evolution
I would like to point out here that human technology has nothing to do with evolution. Not only have all of our notable technological achievements occurred in the last couple hundreds years when human evolution was at its slowest (early human evolution as we know it today dates back at least 5-7 million years, and it was during this several million year period when all the genetic evolution you speak of happened), I would argue that human spaceships and computers are no more sophisticated to us than a mushroom garden and ventilation system are to a termite. I could be wrong here but it seems as if you are under the impression that evolution is striving towards something... That humans are somehow intrinsically better than lions or sharks or beetles. On the contrary, each of these creatures is not significantly more or less adapted to their environments as we are to our own, and in many ways these creatures possess features which are beyond our own.
I shall leave you with one of my favorite quotes:

&quot;We need a wiser and perhaps a more mystical concept of animals. We
patronize them for their incompleteness, for their tragic fate having
taken form so far below ourselves. And therein we err, and greatly
err. For the animal shall not be measured by man. In a world older and
more complete than ours, they move finished and complete, gifted with
extensions of the senses we have lost or never attained, living by
voices we shall never hear. They are not brethren, they are not
underlings. They are other nations caught with ourselves in the net of
life and time, fellow prisoners of the splendor and travail of the
earth.&quot;

–Henry Beston, in The Outermost House
I don't have a dog in this fight, and I could very well be falsely assuming that you think this particular way when you in fact don't (you only wrote 4 lines after all, it's hard to glean much from that), but I wanted to make sure that these concepts were clear either way, particularly for any future visitors who might get the wrong impression. :)