I believe the idea is as follows.
1. Suppose you have contributed to projects A, B, C, D, and E.
2. When someone looks at your profile, they see A, B, C, D, and E listed in a vertical list, apparently sorted by how many contributions you have made to each.
3. You decide that you want the world to know you disavow your contributions to one of these, say, B.
4. You fork the project disavow/above-repository.
5. You make a branch, make some commits, and push them, and then make a pull request. Apparently disavow/above-repository will accept your pull request.
6. disavow/above-repository then appears in your contributions list.
7. Keep making commits to move disavow/above-repository up the list until it is between B (the project you wish to disavow) and C.
8. Now when people look at your contributions list, they see:
A
B
disavow/above-repository
C
D
E
I'm not sure what you are supposed to do if you want to disavow a second repository. Maybe they need to make a disavow/below-repository project too.
The idea of disavowing contributions is an interesting one, although it is probably something best handled by convincing Github to support a mechanism for it. More generally, it could be useful to have a mechanism to explain your relationship to a repository you have contributed to. On a project page, you should be able to view the explanations from all the contributors, and on a person's profile, the list of projects they contributed to could also list their explanation.
