Well, if you listen to the little cantiga, you'll get that 'sabem bem nadar' must mean can - i.e. know how to swim well.
Why not podem? that also means can, right? Yes, but mostly in the sense of to have permission, more like may. So, podem nadar aqui, means they can - i.e. may, are allowed to swim here.
Let's make some more examples:
Can as in know how to do
- Sei falar português, mas não sei falar francês. I can speak Portuguese, but I can't speak French
- O meu irmão sabe cozinhar muito bem. My brother can cook very well
- Os meninos ainda não sabem nadar. The children can't swim yet
Can as in have permission
- Posso fechar a janela? Can I close the window?
- Nao podes sair mais cedo. You cannot leave earlier
- Podemos trazer os nossos caes? Can we bring our dogs?
Can you think of any more examples that would be relevant for you?
Who would think you can learn much from a little children's song? (and for those of you ready to delve into the prepositions, note the use of para - cabeca para baixo, rabinho para o ar and the truncated p'ró = para o as it is said /sung so quickly!)