This mishnah contains two separate sections dealing with two different topics, and we will take each one on its own. The first topic is finding produce along the road, and it raises two questions: may the finder keep the produce for himself, and if he may, must he tithe it before eating it, or may he eat it on the road just as it is?
The basis of the permission: the owner's despair
Permission to keep a found object depends on whether we can confidently assume that the owner has given up hope of getting it back. If it is reasonable that the lost item will be returned to its owner, for example when it bears an identifying mark, that is, a mark that proves conclusively that the item is his, the owner does not despair, since he has the ability to prove his ownership and get his property back. In such a case the item is not ownerless, it remains the property of its original owner, and the finder may not keep it.
On the other hand, when there is despair, that is, when we can confidently assume that the original owner has already given up hope of recovering his lost item, the lost item immediately becomes ownerless, and therefore the finder may keep it for himself. At that point only one question remains: must he tithe it before eating it?
Figs and dried figs found along the road
The mishnah deals with two cases:
"Ketzi'os" - split figs laid out to dry. A person found dried figs on the road, even right next to a field that is private property in which such figs are laid out to dry.
A fresh fig - a fig tree leans out and hangs over the road, and someone walking along the road finds a few figs directly beneath that tree.
In both cases the finder may keep the figs for himself, even though it is quite likely that the dried fig came from the nearby field where similar figs are being dried, and that the fresh fig fell from the tree above. The reason, as the Bartenura explains, is that figs are soft and pulpy, and once they fall they lose their shape to some degree, so there is no definite indication that they in fact came from that tree or that field.
For this reason we assume that the owner of the fig tree or the owner of the field of drying figs despairs and gives up hope of getting his property back. Once the produce has become ownerless, the finder is permitted to keep it as far as the laws of theft are concerned.
Technically, there would have been room to obligate him here in the mitzvah of returning a lost object, since it can be assumed with high probability that the dried fig belongs to the field of drying figs and the fresh fig to the tree leaning directly above it, both of which are private property. But since the finder finds a justification for himself, saying that there is no conclusive proof that this fig belongs to those owners, he will in the end keep it for himself, and therefore we can assume that there was despair, and that the produce is ownerless.
And since that is so, the figs are exempt from tithes: whoever finds the fig or the dried fig may eat it on the road without tithing it first, since ownerless produce is exempt from tithes.
It is worth noting: ownerless food is exempt from tithes only if it became ownerless before the completion of its processing, that is, before that particular fruit was fully prepared. But if it has already reached the stage of completed processing, then even if a person explicitly declared his crop ownerless, the finder must tithe it, since it has already reached the stage at which the obligation of tithes takes effect.
And with fresh figs that fell from the tree, they certainly have not reached the completion of their processing, since they dropped without ever having been gathered. The same is true of figs laid out to dry: as long as they have not dried completely, it is clear that they have not reached the completion of their processing. In all of these cases the finder may keep them, since we assume the owner despaired and abandoned them, and he is exempt from separating tithes, because they are ownerless.
"Uvazayis uvecharuvim":
"Uvazayis Uvecharuvim" - if he found the fruit directly beneath the olive tree or the carob tree, he must return it to its original owner. The Bartenura explains: olives and carobs are hard, firm fruits, and when they fall from the tree their form does not change, unlike a fresh fig. Because of this one can clearly identify that the olives match the olives on the tree and the carobs match the carobs on the tree, and this serves as a distinguishing mark. The owners do not despair and do not give up hope of getting back what is theirs, and therefore the finder must return the fruit to them because of the laws of theft, and he certainly may not eat it without tithing, since it is not his.
"Matza grogros":
"Matza grogros" - one who finds dried figs on the road can be certain that they did not fall from the tree, since they are already dried. They carry no mark or identifying feature that would clearly identify them, and therefore he may keep them and eat them. The only question is whether he must tithe them before eating them along the way.
This depends on whether the dried figs have reached the completion of their processing. As we learned in the last mishnah of the first chapter, the completion of processing for dried figs is "misheyeidoshu" - from the time they are trodden and packed and pressed together into the vessel. Dried figs that have not yet been pressed into a vessel have not reached the completion of their processing. And one who finds a dried fig on the road - who knows whether it came from a vessel that had already been pressed, or perhaps from before it was placed into the vessel for pressing. No one knows.
Therefore the mishnah rules that we follow the majority:
"Im darsu rov bnei adam" - if most people have already trodden their fig cakes into the vessels, "chayav" - the finder must tithe this fig cake before eating it. (Note the difference: the "chayav" stated regarding the olive and the carobs means an obligation to return them to the owner, whereas this "chayav" means that he may keep it, but he is required to tithe it.)
"V'im lav" - if most people have not yet trodden their fig cakes into the vessels, we may assume that this fig cake came from the majority whose processing was not completed, "patur" - it is exempt from the separation of tithes before eating, since we follow the majority, and the majority has not reached the completion of processing, so it turns out that he found it before the completion of its processing.
"Matza pilchei develah":
"Matza pilchei develah" - pieces of a fig cake. As we learned in the first chapter (in the sixth mishnah, and perhaps really in the eighth mishnah), pressing the figs into a cake is the final stage: once they have been pressed into a cake they are finished and ready to eat - one breaks off a piece of the cake and eats it while walking along, and one even coats it with juice to give it a shine.
It emerges that one who finds pieces of a fig cake knows clearly that they have reached the stage of completion of processing. And although he may keep them, since there was despair and they bear no identifying mark, nevertheless he must tithe them before eating. This is the language of the mishnah: "Matza pilchei develah, chayav, sheyadua shehein b'davar gamur" - that these pieces come from fruit that has reached the completion of its processing, since all fig cakes have reached the completion of processing.
The Second Part - Feeding Carobs to Animals:
Here the first topic comes to an end, and we move to an entirely new subject - and in fact we return to the topic we dealt with in the first mishnah of this chapter. There we learned about someone bringing figs through his courtyard in order to dry them: since the figs have not reached the completion of their processing, because his intention is to dry them, anyone may take from them and eat even in the courtyard without tithing them - anyone except the owner himself. The owner may not eat from those figs, because it looks to an observer as though he is eating his own figs in their untithed state without tithing, and it is hard to claim that his intention is to dry them and not to eat them at the very moment that he is eating from them.
Now the mishnah continues with the same matter and discusses carobs. Carobs too were dried like figs, and while they were in the process of drying it was not unusual to feed them to one's animals. The question, then, is whether the owner himself may bring carobs down from the drying roof into the courtyard and feed them to his animals there.
And the mishnah answers that he may: "V'charuvin, ad shelo k'nasan" - and carobs, as long as he has not gathered them into a pile. As we learned in the first chapter (in the sixth mishnah), the completion of processing for carobs is their drying and their being gathered into a pile. As long as he has not piled them up on the roof of the building, they have not reached the completion of their processing, and the carobs are still drying. Therefore "Morid mehem la'behemah" - he may take from those drying carobs and feed them to his animals even in the courtyard, "u'patur" - and he need not tithe them before feeding them to his animals. For everyone may eat from them except him: his animals may, and he himself may not.
And why? "Mipnei shemachazir es hamosar" - because they have not reached the completion of their processing, and these carobs are not to be regarded as a separate harvest in their own right. For any carobs that his animals do not eat, if he brought down more than he needed, he will simply return the surplus and take what is left back up to the roof to continue drying. This proves that these are not a separate harvest from the carobs drying on the roof, but rather it is all one large harvest, and he is merely feeding a portion of it to his animals. Therefore the animals may eat from these half dried carobs even in the courtyard without any tithing, and whatever is left he can return to the roof so that it will continue to dry.
And incidentally, exactly as in the first mishnah: if he is standing on the roof, he too may eat from these carobs, since they are not in his courtyard, for on the roof it is evident to all that he is drying them, and therefore this is a casual eating from produce that has not yet reached the completion of its processing.