Really, the Nobel Peace Prize only has whatever significance people want to give it. It does give the winner a lot of money, but it does not make people have to agree with what that person says or advocates.
The Nobel Peace Prize is simply given to the person that the prize committee thinks did the most to advance peace in the world in the past year. This is a very subjective judgement, of course.
Winning the Peace Prize does not mean that the winner's ideas will be heard. For example, the most recent Peace Prize winner is Liu Xiaobo, a Chinese dissident. Although he won the Prize, the Chinese government is not changing in the ways he wants and other countries are not pressuring the Chinese to do so. This shows that the prize does not really change things by itself.