What does it mean to have 3 out of 6 genetics markers when getting test results as a kidney donor?

Variable. Hla antigens are a major factor that drives the rejection response to transplant organs. Matching refers to the number of hla antigens identified in recipients and donors; and how many are the same. Commonly six antigens; two for hla a, two for hla b, and two for hla dr are typed matched for kidney transplant. So a 3/6 match means half the hla antigens are the same.
You may be related. There are 6 genetic markers which seem to play a more important roll than the rest of the genome in promoting organ rejection. You get 3 of these markers from each of your 2 parents. So everyone shares at least 3 markers with each parent. You can share up to 6 and this ultimately depends on the current and ancestral relationship between the donor and recipient.