Before us is mishnah 4 of chapter 8 of Maseches Eduyos, and in it we meet Rabbi Yosi ben Yoezer. Yosi ben Yoezer, as we recall from Maseches Avos, was the first of the five Pairs, and a nasi at the beginning of the Second Temple era, shortly after Shimon HaTzaddik. It emerges, then, that he lived hundreds of years before that famous "bo bayom" (that very day) which Maseches Eduyos records. The simple explanation of what is happening here is that the Sages of that day are recalling testimony that he gave in his own time, and they quote his words almost in their exact original wording, in the Aramaic in which they were said. Others explained that the words were said in Aramaic because it was important that they be known to the common people.
"He'id Rabbi Yosi ben Yoezer ish Tzreidah":
Yosi ben Yoezer, the man from Tzreidah, was the leading rav of Tzreidah. He testified about three things, and all three were leniencies - and for that reason, as we will see at the end of the mishnah, he was called after his leniencies "Yosi shareya", Yosi the permitter.
The first leniency - "al ayil kamtza dechen":
There are species of locusts that are kosher and species that are not kosher. Yosi ben Yoezer testified that the species called 'ayil' is kosher for eating, and this is the tradition he received. The technical details, including the Gemara's extensive discussion of whom he came to disagree with, go beyond the scope of our lesson, and here we will suffice with explaining the difficult Aramaic words.
"Ayil" - the name of the particular species of locust (the word itself means a deer).
"Kamtza" - locust in Aramaic, as in "Kamtza and Bar Kamtza" of the well known story sometimes read on Tishah B'Av.
"Dechen" - pure, in the plural.
The underlying principle is that the letter zayin in Hebrew frequently becomes a dalet in Aramaic: "zach", as in "shemen zayis zach" (pure olive oil), becomes "dach" in Aramaic, pure. And just as the verses call kosher animals 'tehorim' (pure) - not in the sense of tumah and taharah, but in the sense of being permitted to eat - so too the meaning here: this locust is pure, that is, kosher for eating.
The second leniency - "v'al mashkei beis mitbechaya d'inun dachyan":
The plain meaning is that the liquids in the slaughtering area of the Beis HaMikdash are pure. To understand the matter, we must first note that there are four categories of things that can contract tumah:
A person.
Vessels.
Foods.
Liquids.
Rav and Shmuel disagree as to whether liquids contracting tumah is a Torah law or a rabbinic law. The halachah was decided in accordance with Rav, and as the Rambam understood it, that they contract tumah by Torah law. However, by Torah law liquids do not transmit their tumah further to other things - that is, if a tamei liquid touched food, the food remains pure by Torah law. The transmission of tumah from liquids to other things is a rabbinic decree alone, and in this everyone agrees.
A side note, to prevent confusion: we are not speaking here about the seven liquids that make foods susceptible to tumah (the mnemonic: yad shachat dam). That is an entirely separate rule, according to which foods do not contract tumah unless they were first made susceptible by one of those seven liquids. Our discussion here concerns liquids that become tamei and transmit tumah further.
The point of the Mishnah is that in the Beis HaMikdash there was a place where the sacrifices were skinned and cut up. After the animal was slaughtered and its blood received - slaughtering, receiving the blood, carrying it and sprinkling it on the altar, which are the essential services of a sacrifice - there is an entirely separate matter: the sacrifices have to be eaten or burned, and for that the hide must be removed, the meat cut into its portions, and sometimes the intestines must first be cleaned and emptied of their waste before the burnt offering is brought. For this purpose there was a special area in the Beis HaMikdash, containing tables, hanging hooks and rings, for processing the animals after they were slaughtered. Understandably, a great deal of liquid collected there: blood, water from rinsing the innards, and the like.
The novelty of the Mishnah is that even though the Sages decreed that liquids transmit tumah, that rabbinic enactment does not apply in the slaughtering area of the Mikdash. That is the essence of the matter.
And in the wording of the Mishnah itself: "V'al mashkei beis matbechaya" - concerning the various liquids found in the slaughtering area on the northern side of the Azarah; "d'inun dachyan" - that they are pure, again from the word "dach," meaning "clear," that is, that they do not pass tumah on further, and perhaps do not even become tamei at all.
Indeed, the Rambam rules that in general liquids become tamei by Torah law and transmit tumah only rabbinically, but in the slaughtering area there is a special, separate law: by Torah law the liquids there do not become tamei at all. That is the Rambam's ruling, and that appears to be the practical halachah.
The third leniency - "Ud'ikrav b'meisa mistaav":
The plain meaning is: one who touches a corpse becomes tamei. But this we already know from the verse, and there is nothing novel in it that would require testimony. His intent, then, is to the reverse, the other side of the coin: true, one who touches a corpse is tamei, but when a doubt arises - whether he touched the corpse or not - and that doubt arose in a public domain, in a place frequented by many people (three people or more), the rule is "a doubtful tumah in a public domain is pure."
But this rule too, though it is not an explicit verse, is agreed upon by all and known to all. What, then, did Yosei ben Yoezer come to add?
The answer is that before Yosei ben Yoezer's testimony, people held: it is true that a doubtful tumah in a public domain is pure, but "we do not rule so publicly" - we do not publicize it, because it confuses people. For in the previous Mishnah it was explained that in a situation of doubt we follow the stringency. And here, for example, two people are going up to the Mikdash for the festival, and there are two paths before them, and it turns out that a corpse is lying on one of them. They ask the man: which path did you take? And he answers: I do not know. Here we have a doubt as to whether he passed by the corpse.
According to the rule the ruling is: a doubtful tumah in a public domain - and this was a public path - is pure, and he is permitted to bring his sacrifices. This seems to contradict following the stringency in cases of doubt, and as a result people would err and come to treat the matter lightly, not taking the laws of tumah and taharah seriously. That was the concern. Yosei ben Yoezer came and testified: we are not concerned about that, we publicize the matter, since people understand and will not come to treat it lightly.
A second explanation for why he acted this way: a person who thinks he is tamei may in the end burn Terumah and the like, which is a Torah prohibition. Therefore he must know that he is not tamei at all, since a doubtful tumah in a public domain is pure. For this reason he said: we publicize the matter, and everyone must know that a doubtful tumah in a public domain is pure, and he is tamei only when he knows with certainty that he touched tumah.
"Yosei Shar'ya":
These are the three leniencies that he introduced and ruled:
The 'ayil' locust is kosher to eat.
The liquids in the slaughtering area of the Beis HaMikdash are tahor.
A case of doubtful tumah in the public domain is tahor, and this may be ruled publicly.
And because of these three things "karu leih" - they called him - "Yosef sharya" - Yosef the permitter, the man of the lenient rulings. This nickname was not necessarily meant as a compliment: it implied that he was too lenient, that he did not carry enough weight, that he permitted things. In practice, everything he did was perfectly correct: the halachah follows him, and the Sages even said "koach d'heteira adif," that there is an advantage in the ability to permit things to people. Even so, the sense of the Mishnah here is that consistently innovating on the lenient side is not something admirable.
The Gemara even brings a separate precedent for this: an Amora named Rabbi Yehudah Nesiah, mentioned in Avodah Zarah 37, who had already permitted two things in other contexts, refrained from introducing a third leniency - on the strength of the principle that emerges from our Mishnah.
In summary: in our Mishnah, Rabbi Yosef ben Yoezer of Tzereidah testified about three things, all of them leniencies: that the 'ayil' locust is kosher; that the liquids in the slaughtering house of the Beis HaMikdash are tahor - that the rabbinic decree transmitting tumah through liquids does not apply there, and according to the Rambam they do not even become tamei on a Torah level; and the public ruling that a case of doubtful tumah in the public domain is tahor. Because of these three leniencies he was called "Yosef sharya," and from here the Gemara learned that even though koach d'heteira adif, it is not fitting to innovate consistently on the lenient side.