It doesn't mean _nothing_ -- it's just prone to the same type of problems and edge cases affecting pretty much every attempt at categorizing in a very complex system.
To me it means _nothing_ when the end-class you use is very ambiguous. A classifier should be as specific/differentiated as possible or else, it's useless.
You mentioned in another comment that haplogroups would be too foreign a classification for you, but that would likely be the most specific/differentiated classifier.
If somebody says they're a "quarter French" -- putting aside whether that's interesting or not -- do you believe that's meaningless? Do you demand them to specify whether it was one of they have Gallic roots or if it was one of the Germanic tribes that invaded from the north 1500 years ago or something else altogether?
I think the point of this test is to try to capture the spirit of what Americans have done for a long time, which is to try to describe their heritage in fractions using nationality of a distant (but not too distant past) as a rough guide.
And in the same way that your genome might prove more complicated than naming fractions by nation, somebody might say "My grandfather came to the USA from France... but he was part of a second generation immigrant community from a Greek-speaking part of Sicily who emigrated en masse to Alsace, which was located in Germany, not France at the time".
So maybe the DNA test will call that French or German or Italian or Sicilian or Greek or whatever and that might oversimplify it and the test doesn't work as well as somebody whose ancestors stayed in one location and was part of a largely homogeneous population, but that doesn't render the test meaningless. Part of the excitement people derive is that it can sometimes illuminate your ancestral history beyond what is well known. Using the previous example, somebody might not be aware of the complexity of their grandfather's heritage, and might be interested to understand that part of the family has roots in Sicily and not just France.