If I add a new file to a project under TFS source control, it will check out the project file and the corresponding .vspscc file for that project file.
The project file
This file is a holdover from past VSS/TFS implementations, like Paulo Santos posted.
On the solution level, I have found no functional use for these files. In 10 years of using TFS, I have never seen that file altered. You can delete these .VSSCC files, as I commonly do for my closed source solutions.
But if you delete the solution-level .vsscc file, you will get a non-destructive error message on the first time open of the solution file...only after a new branch is created. All subsequent solution opening will not show the error message again.
My TFS setup standards have the solution file alone in the root folder, all projects are under sub-folders. Since those .vsscc files double the number of files in my root, I always delete them.
On a project level, I leave those files, as my team never opens project files directly, only solution .SLN files.
For my team, I prefer programmer ease of opening solutions over that one-time error message.