As is the case with all legal documents, the date that appears on a geṭ is one of the basic requirements for the document to be valid. Somewhat surprisingly, the geṭ need not be delivered on the date that is written in the document, and it will be a valid geṭ even if it is given some time later. This is only true if the couple did not continue to live in close proximity after the geṭ was written. If after the geṭ was written the husband and wife were together (i.e., they could have slept together) then the geṭ is considered a geṭ yashan – an old geṭ – which the Mishna teaches cannot be used according to Beit Hillel, although Beit Shammai permits its use.
The Gemara explains that the basis for the argument between Beit Hillel and Beit Shammai is whether we fear that people will mistakenly think that the date written on the geṭ was the actual day of the divorce, and will assume that any children born to the woman more than nine months after that time were born out of wedlock. Beit Hillel is concerned about this possibility, and therefore only permits the geṭ to be used if no children will have been born since the geṭ was written. Beit Shammai is not worried that this will be an issue.
The rishonim suggest that this disagreement between Beit Hillel and Beit Shammai has its source in their basic positions on divorce that appears on daf 90a. According to Beit Shammai, a man can divorce his wife only if he believes that she has behaved inappropriately in matters of a sexual nature. Therefore we can assume that if he wrote a geṭ he has indicated that his relationship with her is irreparable, and we need not be concerned that they have slept together, even if they had yihud (they were together in a private place). According to Beit Hillel, there are other reasons that a man may divorce his wife, and we would have every reason to think that even after he wrote a geṭ he may change his mind and continue to have marital relations with her, until such time as they get divorced.