Before us is Mishnah 6 in the second chapter of Maseches Eduyos. The opening of the Mishnah can be a little misleading: it reports that Rabbi Yishmael said three things that Rabbi Akiva did not agree with him about, but in practice there are not three separate topics here, only one topic - one that applies to three types of food.
The subject under discussion:
A person takes garlic, crushes it until it becomes something like a paste, places weights on it in order to press it, and the juice drips out slowly and collects in a vessel. In the days of the Mishnah this juice was used as a dip for bread.
One has to understand the background: in the days of the Mishnah the main food was bread - morning, noon and night. To relieve this monotonous menu they used various dips that gave the bread flavor, similar to what is common today with chummus, techinah and baba ganoush. Instead of our matbucha, they dipped in garlic oil and the like.
The decree of the Sages regarding liquids that seeped out:
The Sages instituted a rabbinic prohibition against using, on Shabbos, liquids that drip out on their own from solid foods. The reason for the decree lies in one of the thirty-nine melachos:
The melachah of threshing (dash): extracting something useful from its container. When stalks of grain are harvested from the field, the edible kernels are still attached and sitting inside a sort of small container. They are laid out on the threshing floor, the cow walks in circles dragging a heavy board, and through the force of the friction the outer chaff, which is not needed, separates from the inner kernels. It turns out that the person is removing the inner kernel from its little pocket - this is the melachah of threshing.
The toladah of mefarek: a subcategory of threshing, whose subject is squeezing - removing something from its place. The clearest example is squeezing oranges: inside the orange there are tiny packets of cellulose with liquid inside them, and when the fruit is squeezed the packets open and the liquid comes out of them. Removing the liquid from its place resembles threshing, and it is therefore considered its toladah.
It follows that squeezing a lemon into a cup in order to drink it is forbidden by Torah law. Because of the severity of the matter, the Sages distanced a person further and decreed that one may not use at all liquids that come out on their own, lest a person come to actually squeeze on Shabbos.
What is the law when he crushed it before Shabbos:
Here the question of the Mishnah arises: what is the law if he crushed the food before Shabbos came in? The three foods under discussion are:
Garlic.
Unripe grapes - grapes that have not ripened.
Melilos - wheat kernels that have not ripened, which are soft and sticky.
A person crushes these foods and mashes them, places weights on them in order to press them, and they continue to seep throughout Shabbos. If all the work of crushing and setting the weights was done while it was still day, is it permitted to use the liquid that collected on Shabbos?
The answer is that it is permitted. Although the Sages decreed against liquids that seep out on their own, lest one come to actually crush and squeeze on Shabbos, here the food was already crushed while it was still day, and the liquid comes out on its own in any case. Therefore, even if he were to squeeze it further, that would involve no more than a rabbinic prohibition - and he is not even doing that, since the liquid is already on its way out, and all that is happening is a slow dripping and collecting. For this reason the Sages did not forbid gathering the liquids that come out of items ground while it was still day and using them on Shabbos itself.
The words of the Mishnah:
"Sheloshah devarim amar Rabbi Yishmael, velo hodah lo Rabbi Akiva" - the three matters all deal with exactly the same issue: garlic, unripe grapes and fresh grain kernels. "SheRiskan mibe'od yom" - that he crushed them on Friday afternoon, before Shabbos came in. "Rabbi Yishmael omer: yigmor mishtechshach" - he may finish the crushing before Shabbos, and the liquid will drip on Shabbos and be permitted for use. "veRabbi Akiva omer: lo yigmor" - there is no point in crushing before Shabbos, since even if he does so he will not be able to use the liquid on Shabbos on account of the rabbinic prohibition.
The halachah in practice:
The halachah was ruled like Rabbi Yishmael, and it is permitted. This ruling is somewhat unusual, since the common rule is that in a dispute between Rabbi Akiva and a colleague of his the halachah follows Rabbi Akiva; and Rabbi Yishmael is even considered something of a student of his, so all the more so there was room to rule like Rabbi Akiva. Nevertheless, here, for whatever reason, the halachah was ruled like Rabbi Yishmael.
In summary: If a person ground garlic, unripe grapes or fresh grain kernels while it was still day, he may gather on Shabbos the liquid that seeps out of them and use it for dipping bread.