This mishnah opens with three laws in the halachos of moving muktzeh on Shabbos: picking up a child who is holding a stone, lifting a basket with a stone inside it, and moving impure Terumah together with pure Terumah and with chullin. It closes with the words of Rabbi Yehudah regarding a mixture of Terumah and chullin.
"Notel adam es beno veha'even beyado" - a person may pick up his son even though there is a stone in the child's hand:
The mishnah permits a person to lift his son even though the child is holding a stone, which is muktzeh. The Gemara limits this permission with two qualifications:
Only with a child who longs for his father, to the point that Rashi explains he is liable to become physically ill if his father does not pick him up. Others explain that the child's distress and pain alone is enough to permit picking him up.
Only with a stone. If the child were holding a coin, which is something the father has an interest in, the father would not be allowed to lift him while the coin is in his hand, out of concern that the child might drop it and the father would come to pick the coin up.
"Uchelkalah veha'even besochah" - and a basket with a stone inside it:
The mishnah permits lifting a basket even though a stone is lying inside it. The Gemara establishes that this is speaking of a basket that contains fruit, so that the basket is a base both for a forbidden item, the stone, and for a permitted item, the fruit, and therefore it may be lifted.
However, the Gemara narrows the permission to moist fruit, such as berries and grapes. The reasoning is that ordinarily he should empty the basket of both items together, and then carry the basket without the muktzeh and the fruit without the muktzeh, ridding himself of the stone by throwing everything out. But with moist fruit this is not possible, since the fruit will end up getting dirty, and therefore moving the basket was permitted. With dry items, though, such as hard nuts and the like, he should throw out the stone together with the edible fruit, and he may not carry the basket without first throwing out the stone.
The Gemara adds further that even with such moist fruit, if he is able to push the stone off to the side, he is obligated to do so. Because of these requirements, the Gemara establishes the mishnah as speaking of a case where there is a hole in the basket and the stone plugs it: since it serves a function, it is subordinate and secondary to the basket, and in such a case it is not muktzeh at all.
"Umetaltelin Terumah temei'ah im hatehorah ve'im hachullin" - and one may move impure Terumah together with pure Terumah and with chullin:
Impure Terumah is muktzeh, since it has no use and is designated only for burning. The mishnah permits moving it in a basket and the like together with pure Terumah and with chullin, which is not Terumah at all. Here too the Gemara establishes conditions:
The pure Terumah is lying underneath and the impure on top, so that the pure cannot be reached. But if the pure were lying on top, he would have to take only the pure, and there would be no permission to move the basket with the impure Terumah inside it, since he could have taken the pure without dealing with the impure at all.
We are speaking of moist fruit and the like, which would get dirty if he threw them out. Otherwise, he would have to throw them out, as explained above.
A further qualification: if he needs the place where the vessel is lying, he may move it in any case, because he needs its place.
The words of Rabbi Yehudah - "Af ma'alin es hameduma be'echad ume'ah" - one may also raise up the mixture with one in a hundred:
The mishnah concludes with a law that is similar but not really connected to the laws of muktzeh, even though it does involve moving something. Terumah that fell into a hundred times its volume of chullin is nullified, but a person bears the responsibility to remove the amount that fell in so as to give it to a kohen.
And since the mixture is nullified, one may eat from it even before he removes that amount which fell in, provided that he designates in his mind where it is going. And since he was able to eat from the mixture on Shabbos without actually removing that amount, removing it in order to give it to a kohen is not included in the category of separating Terumah on Shabbos, and it does not carry the appearance of fixing something that separating Terumah ordinarily carries, since he was permitted to eat even without separating.
In summary: in this mishnah we learned three permissions to move objects and their conditions: picking up one's son with a stone in his hand - only with a child who longs for his father, and only with a stone and not with a coin; lifting a basket with a stone inside it - when it contains moist fruit, and according to the Gemara's conclusion when the stone plugs a hole in the basket and is subordinate to it; and moving impure Terumah together with the pure and with chullin - when the pure is underneath, with moist fruit, or when he needs its place. And finally, the words of Rabbi Yehudah that one raises up the mixture with one in a hundred, since removing the amount does not constitute separating Terumah on Shabbos.