Read this on my lab report "low positive thyroglobulin antibodies are seen in assymptomatic population" what does that mean in real terms?

Not diagnostic. In general, lab tests are used to support a clinical diagnosis and thus a positive test per se does not provide a diagnosis without abnormal physical findings or symptoms. On many occasions, an abnormal lab test is not associated with any disease condition especially when the value is only slightly abnormal. If you do hundreds of tests on a healthy person, you will likely find something abnormal.