Sensitivity = rule out = "snout". A highly sensitive test is one that does not miss any true positives, meaning there are no false negatives.
100% sensitivity means everyone with HIV tests positive for HIV. There will be many false positives, but no false negatives. Therefore, a highly sensitive test "rules out" a disease because if the test says you don't have it then you probably don't have it.
Specificity = rule in = "spin". A highly specific test is one that has no false positives.
100% specificity means everyone that's HIV free will test negative for HIV. There will be many false negatives, but no false positives.