When you gain 100,000 points you get a permission to edit any post of any user.

As Paul said they are only an indicator of your italki community activity. Users with a high number of points tend to be either serious language learners or helping other learners a lot. You can see in Paul's profile that he has a very high number of italki points but didn't post a lot of notebook entries, that means he must be quite active in the discussion forum or in helping other users to learn English, otherwise, he wouldn't have that many points.

Precisely... nothing. They merely show how active you have been on the site.

They can be exchanged for valuable prizes!  No, really!