Good question.

In astrobiology (and I think also in biology and most of chemistry) it means any molecules that contain carbon, with a few exceptions (exceptions include carbon dioxide and diamond - they don't count as organic). Strange definition, perhaps, but I'm certain that's what it means in astrobiology.

Organic molecules are not necessarily in living things and, indeed, interstellar dust clouds contain huge quantities of amino acids and other organic molecules which most astronomers believe have never been near a living thing.