To understand the meaning of this mishnah, we must first note what the Mishnah teaches in chapter 4 of Maseches Taharos: saliva found anywhere is suspect as possibly having come from a person who is tamei, and therefore if it touched Terumah, the Terumah becomes tamei and must be burned. The same applies to vessels that are found: we assume they are tamei.
The novelty of Jerusalem:
Our mishnah deals specifically with Jerusalem, and its law is an exception: "Kol ha'rukin ha'nimtza'in bi'Yerushalayim tehorin" - saliva found in the city is tahor, and we do not suspect that it came from a zav or a zavah, whose saliva conveys tumah to people and vessels.
There are two reasons for this:
Following the majority: In Jerusalem one may follow the majority, and most of the people there are not tamei.
The eating of kodashim: Since kodashim were eaten throughout the city, those people who were tamei were careful to keep away from the public areas.
"Chutz mi'shel shuk ha'elyon" - the view of Rabbi Meir:
The mishnah qualifies this and excludes saliva found in the upper market. Why?
Non-Jews lived in the upper market, and the Sages decreed that they have the status of a zav. This decree is rabbinic only, since a non-Jew who is a zav is not a zav by Torah law.
Others say that this was the area in which Jewish zavim also circulated, and their tumah is by Torah law itself.
This is the view of Rabbi Meir.
The view of Rabbi Yosi:
Rabbi Yosi distinguishes between the rest of the year and the time of the festival:
During the rest of the year: "She'b'emtza tamei v'she'ba'tzedadin tahor" - at a time that is not Yom Tov, most people in Jerusalem are not tahor. In the middle of the road, in the central area of the street, the crowds walk, including zavim and zavos, and people are not so careful about tumah during the rest of the year; therefore saliva found there is tamei. Along the sides of the road, however, those who are tahor are careful to walk, and therefore saliva found at the sides is tahor.
At the time of the festival: "U'vi'sh'as ha'regel she'b'emtza tahor v'she'ba'tzedadin tamei" - at the time of Yom Tov the law is reversed, for everyone is careful to purify himself for the festival as much as he is able, and most people are tahor and they are the ones who walk in the middle of the road. Those who are tamei are the minority, and "mipnei she'hen mu'atin mistalkin la'tzedadin" - they move off to the sides and avoid walking in the central area. Therefore saliva found at the sides of the road at the time of the festival is tamei.
In summary: While everywhere else saliva that is found is considered tamei and conveys tumah to Terumah, in Jerusalem it is tahor - because we follow the majority, and because the eating of kodashim throughout the city kept those who were tamei at a distance. Rabbi Meir excludes the upper market, where non-Jews lived (whose status as a zav is rabbinic) or where Jewish zavim circulated (whose tumah is by Torah law). Rabbi Yosi distinguishes between the rest of the year, when the majority are not tahor and they walk in the middle of the road, and the time of the festival, when the majority are tahor and the tamei minority moves off to the sides - so that the law of saliva found in the middle of the road and at its sides is reversed.