I think you'd have to read the article to get the best understanding. I'll try to give a summary though.
Basically, the scale isn't meant to assess for autism exactly. It's based on results that have found autism to have genetic links, so the scale is meant for genetic family of autistics to test for autism-like traits. They call this typifying concept Broad Autism Phenotype (BAP) and has three personality characteristics: 1) aloof, 2) rigid, & 3) pragmatic language. They define the characteristics as follows:
aloof personality is defined as a lack of interest in or enjoyment of social interaction; rigid personality is defined as little interest in change or difficulty adjusting to change; and pragmatic language problems refer to deficits in the social aspects of language, resulting in difficulties communicating effectively or in holding a fluid, reciprocal conversation.
People that meet the researchers' criteria for BAP tend to have fewer "high-quality intimate relationships" and "more deficits in use of social language" than parents of children with Down's Syndrome. I didn't see them make any comparison to allistics or other groups, but I skimmed the article, so maybe they did.
Regarding the scale: The researchers administered the scale to a nonrandom sample of 2 populations: 1) parents of diagnosed autistics from an established Autism Registry and 2) parents of allistics with no first-degree autistic relatives. They administered a structured clinical interview to the first group to assess for BAP. This created two groups: 1) BAP present and 2) BAP absent. In other words, the former were clinically deemed to have autism-like personality traits, and the latter were deemed to not. The group of parents with no first-degree relatives served as a control group. They then administered the BAP scale you took to all of the participants and got the results presented in this histogram. As you can see, the scale matched up well with their clinical assessment, so the scale seems to be working properly.
As far as what it means: The score is just a measure of the presence of those 3 traits. The higher the score, the more present they are. One would expect autistics to have higher scores that the BAP group, but I didn't see if they said that and there may be some validity issues with that idea anyway.
It would be weird for autistics to score lower than the BAP group though. Additionally, it's not meant to diagnose autism, and BAP isn't really a diagnosis. It's type they made up using DSM4 criteria of autism. Anyway, if your scores fall with in the range of the little black tails on top of the BAP present group, then you may meet their criteria for BAP. If your scores fall within the tails of either of the other two groups, then you would likely be more similar to them in regards to BAP. However, the sample was nonrandom, so we can't say that with nearly decisive confidence.
Layman's answer regarding your particular scores: There's some evidence that hints you might be deemed BAP if they clinically interviewed you. This could possibly give you some insight into your social life if you tend to have less close friends and difficulty picking up and using communication in person.
Street answer: You might be kinda autistic, which may explain some problems you have with people. It doesn't necessarily mean you are kinda autistic, fully autistic, or neither. If you would like to try other autism tests, check out the Helpful Resources link in the side bar and feel free to share your results.