As usual, these are not technical terms so everybody uses them his way.
Usually, including myself, dirty is used for animalic musks, which, as the name suggests, smell distantly like some animal, skin, sweat, sometimes even slightly urinous. If used in large quantities, these substances can really suggest dirty bathrooms or lack of hygiene, but in the right quantity and with the right accompanying material they can give a sense of warmth, of lived in that can be quite enjoyable. Sometimes, other materials, like spices, can give the same impression and are thus referred to in this way (eg cumin, or sage).
One problem with musks is that people have different sensitivities to each molecule, so what to one person is "warm and sexy" could be "urinal" to another.
Should you have access to them, useful perfumes to highlight these aspects could be Lutens Muscs Koublai Khan or even Kiehl's original musk. Or YSL Kouros (though perhaps not in the very latest reformulation).