This Mishnah discusses the laws of a mikveh. A mikveh is a body of water which a person has to dip into. He has to immerse in order to purify himself or an object. A mikveh is defined as 40 se'ah of water collected naturally in the ground. A se'ah is a measurement of water. That water has to rain directly into the mikveh. It has to be direct rainwater. Water collected in a container is known as mayim she'uvim, drawn water. That water cannot be used to make a mikveh. If you have a regular mikveh that's already kosher (valid), with all rainwater that fell into it, and then add mayim she'uvim on top—even all the mayim she'uvim in the entire world—the mikveh is still kosher. But the Hachamim made a decree and said that if a certain amount of mayim she'uvim was added into the mikveh before it was 40 se'ah, before it was full, then the entire mikveh is disqualified, even if afterward regular rainwater amounted to 40 se'ah.
We'll have a mahloket (dispute) about how much mayim she'uvim, when added into a mikveh before the 40 se'ah of rainwater, invalidates that mikveh. Hillel omer, says Hillel: a hin, a full hin, which is three kav (a unit of volume) of she'uvim waters, would invalidate a mikveh if it's added in there before the mikveh is used. The word hin is not usually used by the Hachamim. It's a word that's used in the mikra (Scripture), in the pesukim (verses). He could have simply used the words three kav. He could have said it's three kav instead of saying the word hin. So it's not normally a term used. Why did he use it? Because a person who's quoting a Hillel, and it's mesorah (tradition)—it comes from his teacher—has to say it with the same expression that his teacher used. His teacher used the word hin, so Hillel did as well. You have to quote it exactly like you heard it from your rabbis.
The Rambam here quotes his father as saying that they were gerei tzedek, they were converts. They did not have the ability to pronounce every Hebrew letter perfectly, so they used to pronounce the word hin as in. They couldn't say the letter he perfectly, like the people of Edom. As the Bartenura says, quoting the Rambam—or really quoting the Rambam in the name of his father—Shemaya and Avtalyon were people from Edom. So the people of Edom, even nowadays, don't have the ability to pronounce letters correctly. So Hillel, when he was quoting his teachers, who incorrectly called a hin an in, also used the word in, as his teachers used that word. He literally quoted it exactly as his teachers said it: the word in as opposed to hin, according to the Rambam.
Shammai says it would take nine kav of she'uvim waters to invalidate a mikveh in this manner. So Hillel said three kav. Shammai says it is nine kav to invalidate it. The Hachamim say, “Not like the words of this one, and not like the words of that one.” They knew that both Hillel and Shammai were incorrect, but they themselves did not have an answer to how much she'uvim water would invalidate a mikveh. When did they get an answer? They didn't know the law until two weavers who lived in the dung gate came and gave testimony in the name of Shemaya v'Avtalyon, the great rabbis. They quoted Shemaya v'Avtalyon and said that even three quarters of one kav of she'uvim waters would invalidate a mikveh. So a smaller amount of water, according to them, would invalidate a mikveh.
We're quoting these people, their occupation and where they lived, to teach a profound lesson: their profession was weaving, which is a very lowly trade. It's undignified. Even so, they made time to study Torah. They were in the Beit Midrash (study hall), and even the community they lived in—the Sha'ar Ha'ashpot, the dung gate—was a very undesirable area. But no matter what a person's stature, it doesn't matter: they were kove'a itim laTorah, they studied Torah. And not only that, their word was considered worthy of being accepted as law, because they heard traditions from Shemaya and Avtalyon. So anybody has the ability to become part of the mesorah, the tradition, and to pass Torah on to the next generation. When they heard the testimony, the Hachamim—even Hillel and Shammai—accepted the words of these weavers as the halacha, as law.