Mishnah 1 deals with the minimum measures for carrying out on Shabbos: what is the smallest quantity of each item for which one who carries it out is liable, and one who did so unintentionally must bring a korban. We begin with the measure for one who carries out wine.
The measures of liquids for liability for carrying out:
"Yayin" - wine: the measure is the amount needed to mix a cup of wine, such as a cup over which a person recites Birkas HaMazon or makes Kiddush. The Gemara explains that this measure is a quarter of a revi'is: a cup of berachah is a revi'is of a log, and since their wine was very strong, a quarter of that measure - one sixteenth of a log - is the amount for which one is liable for carrying out on Shabbos.
"Chalav" - milk: enough for a swallow, that is, the amount an average person swallows at one time.
"Devash" - honey: the amount customarily applied as a salve to a sore, whether a sore formed on the back of a horse or donkey from the rubbing of the loads it carried, or, according to some explanations, a wound on the back of a person's hand or foot. Even though honey is a food, and the measure for foods is a dried fig, since it is also commonly used for medicinal purposes the halachah is stricter with it, and even that small amount is considered a measure, because it regularly serves this purpose as well.
"Shemen" - oil: the amount needed to anoint a small limb. Which limb is meant? The Gemara explains that it refers to the smallest finger and the smallest toe of a newborn baby, so this is an exceedingly tiny amount.
"Mayim" - water: the amount they needed to add to a kilor, an eye salve of which water was one of the ingredients. That amount is the measure for liability for carrying out on Shabbos.
"U'she'ar kol hamashkin" - and all other liquids: their measure is a revi'is, a quarter of a log.
"V'chol hashofchin" - and all waste water: these too are a revi'is. And for what purpose was waste water needed? At times it was mixed with earth to make mud required for building and the like, so it does have a use.
The Tanna Kamma assumes that these measures were stated for an unspecified case, where the person does not state his intention. But if he did specify and needed an even smaller amount than this, he is liable for that amount as well.
The view of Rabbi Shimon:
Rabbi Shimon disagrees and says: "Kulan b'revi'is" - all of them are a revi'is: in an unspecified case, where there is no particular intention, the measure of all of these is a revi'is, and all the small measures listed are not relevant. "V'lo amru kol hashiurim halalu ela l'matzniehen" - and all these measures were stated only for those who store them away: the small quantities listed, such as milk enough for a swallow and wine a quarter of a revi'is, were stated only regarding one who takes these items and stores them away for that purpose, designating them for that end. For one who designates them for that purpose, that small quantity is considered a measure for him; but for one who does not store them away, the small quantity is not relevant to him, and his measure is a revi'is.
In summary: this Mishnah lists the measures of liquids for liability for carrying out on Shabbos - wine, milk, honey, oil and water, with all other liquids and waste water at a revi'is. According to the Tanna Kamma these are the measures in an unspecified case, while according to Rabbi Shimon the measure of all of them is a revi'is, and the small measures were stated only regarding those who store them away, designating the items for that purpose.