Gittin, Chapter 8, Mishnah 4. This mishnah deals with the concept of a "get yashan," an old get, and we will explain its meaning shortly.
"Beis Shammai omrim: poter adam es ishto b'get yashan, u'Beis Hillel osrin" - according to Beis Shammai, a man may divorce his wife with an old get, while Beis Hillel forbid doing so.
And what is an old get:
The mishnah itself defines it: "kol shenisyached imah acharei shekesavo lah" - that is, the husband wrote the get but did not hand it to her, and they continued to live together as husband and wife. It is enough that they were secluded together even once after the get was written for it to be considered an "old get."
The reason for the prohibition:
The concern is that a child might be born as a result of that seclusion, and people will say that the child was born after the divorce, out of wedlock. True, someone born out of wedlock is fit to marry within the community, but a stigma and a negative association still cling to it, and we do not want such a blemish cast when it is simply untrue: after all, she was not actually divorced at that time, and the child was not born out of wedlock. For this reason Beis Hillel said that a man does not divorce with an old get.
After the fact - a dispute among the Rishonim:
The Rambam: after the fact, if he already divorced her with an old get, the divorce is valid, and she may marry on the strength of that divorce even initially.
Rashi: she should not be permitted to marry on the basis of this get, except in a case where the husband traveled abroad and is not available to write her another get; but otherwise, a new get must be written.
In summary: in this mishnah we learned the dispute between Beis Shammai and Beis Hillel regarding an old get - a get that was written, and after it was written the husband was secluded with his wife. Beis Hillel forbid divorcing with it, out of concern for gossip about a child born from that seclusion, as though the child were born after the divorce. After the fact, the Rishonim disagree: according to the Rambam the divorce is valid and she is permitted to marry, while according to Rashi one may not rely on it except when there is no possibility of writing another get.