"Elles savent nager."

Translation: They know how to swim.

[Dna576533]

Is it wrong to translate" they know swimming"???

[Ripcurlgirl]

Yes.

Savoir means “to know” in the sense of knowing how to do something or knowing something by heart, through mental ability or through a learning process. Savoir expresses the knowledge of facts or reasons about certain things therefore:

Je sais danser → I know how to dance.
Elles savent nager → They know how to swim.

Below is quoted from a French post on the WordRef forum:

• Only savoir can introduce a verb in the infinitive or a subordinate clause, never connaître (e.g., Je sais nager, Je sais que tu es en colère, Je sais quand il sera là).

• Only connaître is used when talking about people, not savoir (e.g., Je connais ton frère).

• Savoir typically means:
  --- to be skilled in some art or profession (e.g., Je sais peindre, Je sais fabriquer des chaises.)
  --- to be capable of, to have the power or talent of doing something (e.g., Je sais compter jusqu'à cent.)
  --- to be aware of something (e.g., Je sais que le ciel est bleu.)
  --- to hold something in one's memory so as to be able to repeat it (e.g., Je sais ma poésie.)

• Connaître typically means:
  --- to have gained knowledge or skill in some domain (e.g., Je connais bien mon métier.)
  --- to have knowledge or understanding of something (e.g., Je connais le sens du mot « désespoir », Je connais la réponse à cette question.)
  --- to be informed about the existence or value of something (e.g., Je connais cette chanson, Je connais la valeur du savoir.)
  --- to know someone (e.g., Je connais Marc, Je connais les gens qui habitent ici.)

Source is here on WordRef