“Au” does not mean “the”*. “Le” (or “la”, or “l’”, or “les”) means “the”. “Au” is the contraction of *“à le” (*“à le” is grammatically incorrect). Similarly, “aux” is the contraction of *“à les”.

In French, the name of a country is indeed preceded by an article. We say “la France, le Portugal, l’Allemagne, les Pays-Bas”. Thus, whenever “le Portugal” is preceded by “à” (which has various meanings), it becomes “au Portugal”; similarly, when “les Pays-Bas” is preceded by “à”, it becomes “aux Pays-Bas”.

Note, however, that when countries which are feminine¹ and singular are preceded by “à”, it becomes “en”: “en France, en Allemagne”. This only occurs with names of countries or regions.

1. Or masculine but begin with a vowel sound.