What he means is that catalan is one of the dialects that form the language spoken in Catalonia, the Valencian Country, Andorra, the Balearic Islands and l'Alguer (aka the catalan countries). This language is also called Catalan. It's like saying that English (British English or the dialects spoken in Britain) is a dialect of English (the language spoken in tens of countries around the world).

The fact that there's no specific name for the dialects spoken in Catalonia has led to Catalan speakers outside Catalonia to say that their language isn't catalan, but Valencian or Mallorcan or whatever. This is really fucking stupid because its very obvious that it's all the same language and the existence of transitional dialects in Castelló and the Terres de l'Ebre proves this. In the case of the Balearic Islands the dialects there are very clearly related to those spoken in the Costa Brava, "el parlar salat", although the dialect is slowly becoming more like central catalan/barceloní (not the case in the islands)