This phrase can be found on the title page of dissertations and theses.
As a book I was reading recently (Making the Implicit Explicit by Barbara E. Lovitts) suggests, this should indicate that the dissertation is not standing alone as the factor on which the candidate is judged.
And if signing off on the dissertation is the last hold the committee has and is equivalent to granting the degree, then it might be presumed that the faculty actually vary their standards for what is acceptable as a dissertation depending on their assessment of the worthiness of the student. (the logic here, if not derived from Lovitts, was certainly sparked by what she was saying.)
One could make an argument that this is ethically wrong, and that all dissertations should be held to the same standard. But I'm not sure that there isn't a good argument on the other side, too.
It has long been my opinion that this might be operating on an unconscious level: if your committee believes that you are capable of doing good work, then they will be predisposed to focus on the strengths of the work. If they believe that you are not up to snuff, they will look for problems. This kind of unconscious dynamic works in all of us.
This suggests that you can profit by taking actions that convince your readers of your worthiness; this includes work on the dissertation, but is not limited to such work. It is a point worth strategizing: what can you do that would make the committee believe that you are ready as a scholar?
I recommend Lovitts' book to any dissertation writer who wonders what the dissertation is supposed to accomplish and how they will be judged. I don't think it provides absolute answers because each professor is different, but I think it provides very good general direction.