Before us is a Mishnah in the fifth chapter dealing with the law of a mixture in which yayin nesech (wine used for an idolatrous libation) became mixed with kosher wine. In brief: such a mixture is forbidden even if only the tiniest amount of yayin nesech fell in. In order to appreciate the novelty of this ruling, let us first review the fundamentals of the laws of mixtures.
Background: the fundamentals of the laws of mixtures:
Dry with dry: By Torah law, a mixture of separate, distinct items - for example, three pieces of chicken, two of which were properly slaughtered and one of which was not - can be considered permitted through the principle of nullification by majority: the minority loses its status and its identity is swallowed up within the majority.
Wet with wet: When the taste of the forbidden substance mixes into the taste of the permitted one, matters are more complex. The rule is "taam k'ikar" - any presence of the taste of the forbidden item is regarded as though the forbidden item itself were present in the mixture, and it is not nullified. The Rishonim disagree as to whether this law is of Torah origin or rabbinic.
As long as the taste is discernible in the mixture, the mixture is forbidden. In the absence of a kefeila armaah, a gentile with a trained palate who tastes the mixture (and today we have no way of relying on one), a basic assumption was established that the threshold of taste perception is one part in sixty: if one part in sixty of the mixture is forbidden material, the mixture is forbidden; and if there are sixty permitted parts against one part of the forbidden substance, the whole is permitted.
When the tastes are identical - a substance mixed with its own kind:
Our Mishnah discusses a case in which there is no possibility whatsoever of distinguishing by taste, since the two tastes are entirely identical: wine and wine, except that one is yayin nesech and the other is kosher wine. By Torah law the rule in such a mixture is nullification by majority - the majority determines the status and the minority loses its identity. The Rabbis were stringent in all cases and required at least sixty permitted parts against the forbidden substance, a rabbinic decree lest one confuse this with a mixture of two different kinds, whose tastes differ.
According to the ordinary rules, then, one might have said that a mixture of permitted and forbidden wine is permitted by Torah law as long as the majority is kosher, and that rabbinically sixty permitted parts are required against the forbidden wine. But since the Torah was so stringent regarding the prohibition of yayin nesech, the Sages were stringent as well and ruled that even the smallest drop of yayin nesech that becomes mixed in renders the entire mixture forbidden.
In practical halachah the matter is somewhat more complex than what emerges from the Mishnah, and it depends on what was poured into what: whether a trickle of the forbidden substance fell into the permitted one or the reverse. In any case, for our purposes here we will say that the mixture is forbidden in any measure, with the presence of any quantity at all of yayin nesech.
The wording of the Mishnah:
"Yayin nesech asur v'oser b'chol shehu" - the wine is forbidden in itself, and it also renders a mixture forbidden when present in any quantity at all; even the most minute amount, like a single molecule of yayin nesech, forbids the entire mixture.
"Yayin b'yayin u'mayim b'mayim - b'chol shehu" - this applies both to wine used for a libation and to water used for a libation. When water is mixed with water or wine with wine, there is no way to taste the difference between the forbidden and the permitted, and therefore the entire mixture is forbidden, regardless of the ratio between the permitted and the forbidden.
"Yayin b'mayim u'mayim b'yayin - b'nosen taam" - here we are dealing with two different kinds, items of different types: if the taste of the forbidden substance is discernible, the mixture is forbidden, and if it is not discernible, it is permitted. The threshold of discernibility is one part in sixty.
"Zeh ha'klal: min b'mino b'mashehu, v'shelo b'mino b'nosen taam":
The Mishnah adds a rule that seemingly contains nothing new: two items with the same taste that became mixed together - even the smallest quantity of the forbidden substance forbids the whole; and two different tastes that became mixed - if the taste is perceptible it is forbidden, and if not it is permitted. However, whenever the Mishnah says "zeh ha'klal," the Gemara asks "l'asuyei mai" - this rule must necessarily be coming to include some additional case. Wine we have already dealt with, and with regard to the other prohibitions the rule is not precise: a substance mixed with its own kind is not forbidden in the slightest quantity, but rather, at most rabbinically, in less than sixty and no more. What, then, does the Mishnah come to add?
The Gemara explains that the rule comes to include another severe prohibition: tevel, produce from which the tithes have not yet been separated. If tevel becomes mixed into produce that has already been tithed, the entire mixture is forbidden. The reason is that produce from which tithes have not been separated still contains within it Terumah and ma'aser. Terumah eaten by a non-kohen carries an extremely severe prohibition, punishable by death at the hands of Heaven, and according to Rashi the same applies to ma'aser as well.
Since on a Torah level a single kernel, a single grain, or a single drop is enough to remove the Terumah from the mixture, we apply the rule "as its permitting, so its forbidding": just as we treat one tiny piece as significant enough to permit the tevel, so too if a small amount of tevel falls into a mixture, the entire mixture becomes forbidden. This is the novel point the Mishnah comes to teach: tevel that becomes mixed with its own kind, with tevel of a different type, or with something that is not tevel at all, forbids the whole mixture.
It is worth noting that the law of tevel differs somewhat from the law of Terumah. Terumah that becomes mixed into non-sacred food is not nullified by a simple majority; it requires more than one hundred parts of permitted food against one part of the forbidden substance. The basis of this law is not our concern at the moment, but it is a rabbinic measure that is different from, and stricter than, the usual measure of sixty.
In summary: this is a basic overview of the laws of mixtures. The subject of mixtures is highly complex, and therefore if a practical question arises beyond what has been discussed here, even if it sounds similar to what has been said here, one should ask one's local Orthodox rabbi.