Robert Peary and Matthew Henson's accomplishment to North Pole?
Are you just asking what it was that these two men accomplished? If so, the answer is that they were the first two people that we know of to reach the North Pole.
There have been a couple of controversies about this feat, however. First of all, when the two returned from reaching the North Pole (this was in 1909) they found that another American was claiming to have gotten there first. This other man's claim was discredited a couple of years later.
There is also some amount of controversy over the fact that Henson never got much credit for being part of the expedition. This was largely because he was African-American at a time when racial equality was not on most people's minds.
Ironically enough, we tend to forget that there were 4 Eskimos along with Peary and Henson. We may remember Henson now, but the Eskimos still don't get much credit...