This mishnah deals with the manner in which a get is given, and to understand it we must first establish three fundamentals:
The husband must give his wife the get with her understanding that it is being given for the purpose of divorce. If she thinks it is some other kind of document, it is not a valid get.
He must give her the get; she may not take it from him.
The get must reach a place that is in her domain - a place where she is able to guard it and control it.
"Amar lah: kinsi shtar chov zeh, o shematzaso me'acharav, kor'ah vaharei gitah - eino get, ad sheyomar lah: ha gitech":
"Kinsi shtar chov zeh" - the husband hands her the document and tells her that it is a loan document, not a get.
"O shematzaso me'acharav" - she finds the document behind his back. The Gemara explains that this refers to a case where he turned his back toward her, so that he is the one giving her the get and she is not the one taking it from him.
In both of these cases, even though she read the document and saw that it was a get - "eino get" - it is not a valid get, "ad sheyomar lah: ha gitech". The husband must explain to her that this is her get, and only once he does so can the document be a valid get.
"Nasan beyadah vehi yeshenah, ne'orah kor'ah vaharei gitah - eino get, ad sheyomar lah: hei gitech":
He placed the get in her hand while she was sleeping, and when she awoke she read it and saw that this was her get - it is not a valid get, until the husband says to her: "This is your get."
"Haysah omedes birshus harabim uzrako lah":
"Karov lah" - she is divorced.
"Karov lo" - she is not divorced.
"Mechetzah al mechetzah" - when the get landed exactly in the middle: she is divorced and not divorced, meaning it is a case of doubt whether the get is valid or not.
The Gemara's explanation of "karov lah" and "karov lo":
At first we would have understood that as long as the get entered within her four cubits, it is considered to be in her domain. However, according to Rabbi Yochanan's understanding in the Gemara, even if the get landed outside her four cubits - if she is able to guard it and he is not able to guard it, such as where a river separates between them - she is divorced and the get is valid. For although ordinarily something located outside a person's four cubits is not considered his, the Sages decreed that here the law should operate this way, in order to ensure that women would be able to receive a divorce.
According to this understanding, the words of the mishnah are explained as follows:
"Karov lo" - a place where she cannot guard the get and he can guard it, and therefore it is not a valid get.
"Mechetzah al mechetzah" - a place where neither of them can guard it, or where both of them can guard it together. In such a case "she is divorced and not divorced," and it is in doubt whether it is a valid get, since both of them have control over it.
In summary: we have learned from the three rulings of the mishnah that the giving of a get requires three conditions: that the woman know that it is a get and not some other document, and therefore the husband must say to her "ha gitech" - both in the case where he said "kinsi shtar chov zeh" or where she found it behind his back, and in the case where he placed it in her hand while she was sleeping; that the husband be the one giving and not she the one taking; and that the get reach a place in her domain, from which follow the distinctions of "karov lah," "karov lo" and "mechetzah al mechetzah," depending on which of them is able to guard it.