Before us is Mishnah 4 in the second chapter of Maseches Kiddushin, which deals with an agent sent to betroth a woman, and with the question of the status of the betrothal when the agent deviated from the wording of his mission with regard to place.
The opening clause - setting the place of the betrothal:
"Ha'omer lishlucho: Tzei v'kadeish li ishah plonis b'makom ploni, v'halach v'kideshah b'makom acher - einah mekudeshes" - one who says to his agent: go out and betroth for me a certain woman in a certain place, and the agent went and betrothed her in a different place, she is not betrothed.
By instructing his agent to betroth a particular woman for him in a particular place, the sender defined the limits of the agency. An agent who went and betrothed her in a different place, even though an act of betrothal was in fact performed, did not keep to the precise mission he was given, namely that the betrothal take place in that location, and therefore the betrothal does not take effect.
The sender may well have good reasons for wanting the betrothal to take effect specifically in a certain place: his acquaintances are there, people there will speak well of him, or whatever the reason may be. Once he expressed his wish that the matter be done specifically in that place, the betrothal is valid only there.
The closing clause - 'mar'eh makom', merely indicating a location:
"Harei hi b'makom ploni, v'halach v'kideshah b'makom acher - harei zo mekudeshes" - she is in a certain place, and the agent went and betrothed her in a different place, she is betrothed.
Here the sender is not setting the place of the betrothal, but rather identifying for his agent where the woman is to be found. Even though he mentioned the name of a place, this was nothing more than an indication of where she is, and not a condition limiting the agency, since he did not say that he wants the betrothal to take effect specifically there. Therefore the betrothal is valid even if it was performed in a place other than where the sender assumed she would be found.
To sum up: the distinction in the Mishnah rests on the question of whether the mention of the place is part of the definition of the agency or a mere indication:
"Tzei v'kadeish li b'makom ploni" - go out and betroth her for me in a certain place: this sets a condition in the agency, and the betrothal takes effect only in that place.
"Harei hi b'makom ploni" - she is in a certain place: this is merely an indication of where she is, and the betrothal takes effect anywhere.