We are in Maaser Sheni, chapter 3. As a rule, a person does not redeem maaser sheni in Jerusalem, but only outside of it, as it says: "ki lo suchal se'eiso" - when the load is too heavy to carry and he is unable to bring the produce itself up, he is permitted to redeem it for money and bring the money up to Jerusalem.
But this verse has another interpretation as well: the word "se'eis" can also be understood as eating - eating the produce. According to this reading, whenever a person is unable to eat the produce he may redeem it, even in Jerusalem itself. For example, produce that became tamei, since maaser sheni that is tamei may not be eaten, and therefore there is room to redeem it even inside the city. Our mishnah, then, deals with the criteria for redeeming maaser sheni that became tamei.
The words of the mishnah:
"Maaser sheni shenichnas liYerushalayim venitma" - maaser sheni that entered Jerusalem and became tamei. This does not necessarily mean that it became tamei after it entered, since below the mishnah will also discuss cases where it became tamei before it entered. In any case, the produce is now in Jerusalem and it is tamei. The mishnah speaks of two types of tumah:
"bein shenitma be'av hatumah" - whether it became tamei through an av hatumah (a primary source of tumah), thereby becoming a rishon letumah, for example a sheretz or a dead mouse that touched it.
"bein shenitma bivlad hatumah" - whether it became tamei through a vlad hatumah, meaning that it touched a rishon letumah, something that had touched an av hatumah, and thereby became a sheni letumah.
"bein bifnim bein bachutz" - whether the tumah occurred in Jerusalem or whether it occurred outside the city and the produce entered afterward. Either way, and at any level of severity of tumah, the mishnah discusses their law.
Beis Shammai say:
"yipadeh veye'achel hakol bifnim" - he redeems the produce and eats it inside Jerusalem. There is an obligation to eat it inside, and it may not be taken outside the city, just like ordinary maaser sheni; even though it was redeemed and became chullin, it is still not taken outside Jerusalem.
"chutz mishenitma be'av hatumah bachutz" - this is the exception: produce that became tamei outside Jerusalem through contact with an av hatumah, and entered the city when it was already tamei. The mechitzos, the walls of the city, did not absorb it, and did not take hold of it to the degree that would require eating it in Jerusalem. Therefore, according to Beis Shammai it may be taken outside the city and eaten there.
Beis Hillel say:
"hakol yipadeh veye'achel bachutz" - in all types of tumah he redeems the maaser sheni and eats it outside Jerusalem after the redemption.
"chutz mishenitma bivlad hatumah bifnim" - unless it became tamei through contact with a vlad hatumah, that is, a rishon letumah touched it, and this happened inside Jerusalem. In such a case we do say that the walls of the city absorbed it, since it entered in a state of taharah, and when it became tamei, it became tamei only through a rishon letumah. Therefore, even according to Beis Hillel it must be eaten in Jerusalem, even after the redemption.
In summary: as a rule maaser sheni is not redeemed in Jerusalem, but from the derashah that the phrase "lo suchal se'eiso" also includes one who is unable to eat, we learned that maaser sheni that became tamei may be redeemed even inside. In the mishnah, Beis Shammai and Beis Hillel disagree about where it is eaten after the redemption, and the crux of the dispute is the power of the walls to absorb: according to Beis Shammai everything is redeemed and eaten inside, except for what became tamei through an av hatumah outside; and according to Beis Hillel everything is redeemed and eaten outside, except for what became tamei through a vlad hatumah inside.