If the husband gave his wife three talaaq then the nikah breaks immediately and there is no way the two can get back together again. This is the strongest form of talaaq.
If he divorces her a third time, she becomes a stranger to him (non-mahram) and she is not permissible for him until she has married another husband and the marriage has been consummated.
Allah says: And if he has divorced her (the third time), then she is not lawful unto him thereafter until she has married another husband. Then, if the other husband divorces her, it is no sin on both of them that they reunite, provided they feel that they can keep the limits ordained by Allaah. These are the limits of Allaah, which He makes plain for the people who have knowledge” al-Baqarah 2:229-230