As ever with French wine nomenclature, the definition of a monopole isn't simple.
If you go by the classic definition, a monopole is just a single holding of land (ie one wine producer). It can be as little as single clos (walled vineyard) or a lieu-dit (a named vineyard) or extend all the way to a whole appellation (eg Chateau Grillet).
Historically French inheritance laws dictate that vineyards are split evenly amongst those inheriting. In areas like Burgundy where holdings are already small that can translate into just a handful of vines for each person, hence why a monopole become even more celebrated (because their is a continuity in ownership).
Importantly, however, a monopole is no guarantee of quality. Like any vineyard, it all comes down to whoever is managing the property. With famous Grand Cru monopoles like like Romanee Conti Romanee Conti and Clos du Tart (which is a Grand Cru, a clos and a monopole), however, this is one term with a certain prestige to it - especially amongst the crowded holdings of Burgundy.
It's amazing the lengths that some winemakers will go to. Fanatical is putting it mildly, sometimes it's downright masochistic.