The Mishna on our daf, as well as the Mishna that preceded it (10a) focus on how a person might take possession of an object that he finds by taking hold of it himself or by claiming it as being on his property. The case in our Mishna describes how a person who sees people running after an ownerless animal to claim it can say “my field has effected acquisition of the animal on my behalf” – assuming, of course, that the animal is on his property. According to the Mishna, if the animal cannot move, e.g. if there is a deer with a broken leg or if there are young birds that do not yet fly, then the individual’s property can take possession for him. If, however, the deer was running normally or the birds were flying, then his statement has no significance.
According to Tosafot, in order to take possession of the animal, the owner of the field would not even need to say “my field takes possession of the animal on my behalf” – if conditions allow the owner to claim the animal it will work automatically. The Mishna only includes this statement in order to emphasize that in cases where conditions would not allow him to claim the animal, even making such a statement would not help him. The Rosh suggests that he needs to make the statement in order to keep the people who are chasing the animal from taking hold of something that he has already laid claim to.
The Beit Yosef disagrees, ruling that the owner of the field must make a public claim to the animal, even if it is in his field. While it is true that the Sages established a rule that, “Dalet amot koneh – the four cubits that surround a person take possession of things on behalf of the person,” even without his laying a claim to them, that is a unique enactment made in order to avoid disagreements. Such an enactment was never applied to the person’s field, however.