You can make notebook corrections, comment on discussion, or commen on notebooks to add up points on italki.com

If you have questions about beta points, you can just click on the question mark next to the beta points. And you can also click on the beta points to get more info.

I may be wrong, but I don't think the points do anything for you besides being a sort of ranking system. For instance, someone could look at your account and see that you have a lot of italki points. They could conclude then that you would be a good language partner or teacher because you are clearly involved in the italki community.