Demai, Chapter 6, Mishnah 6. From here on the Mishnah moves from the discussion of sharecroppers to a different question: how much responsibility rests on a person to make sure that the produce he sells will be kept in its state of purity.
The view of Beis Shammai:
"Lo yimkor adam es zeisav ela l'chaver" - a person may sell his olives only to a chaver, that is, to someone who is careful to eat even his ordinary produce - what is not Terumah - in a state of purity.
Becoming susceptible to tumah:
The Mishnah is dealing with olives that have not yet become susceptible to tumah, meaning that they have not come into contact with one of the seven liquids that render food susceptible. For before something can become impure, it must first come into contact with a liquid - it need not be wet at this very moment, but it must have come into contact with a liquid earlier, and that contact must have been willing, with the consent of the owner of the produce. Only then is it susceptible to tumah.
Even though these olives have not yet become susceptible to tumah, Beis Shammai holds that since olives are not normally eaten as they are without first becoming susceptible, but are destined to be pressed for oil, there is reason to be concerned that if the buyer is not a chaver, he will render the olives impure.
The view of Beis Hillel:
"Af l'ma'aser" - one may also sell to someone who separates tithes. In other words, a minimum requirement is set here: the buyer must be a person who separates tithes, but he need not be one of those who are careful in the laws of tumah and purity, since the olives have not yet become susceptible to tumah, and it is possible that they never will become susceptible - for he may eat them before they become susceptible to tumah.
The Mishnah concludes by noting that "tzenu'ei Beis Hillel" - those members of Beis Hillel who were modest and meticulous in the mitzvos, exceedingly careful in the manner of their fulfillment - would act in accordance with the words of Beis Shammai, and would not sell their olives, even those that had not yet become susceptible to tumah, to a person who is not careful in the laws of tumah and purity.
In summary: in this Mishnah the two houses disagree about selling olives that have not become susceptible to tumah. Beis Shammai forbid selling them to anyone but a chaver, out of concern that they will ultimately be pressed for oil and become impure in the hands of someone who is not careful. Beis Hillel permit selling even to someone who merely separates tithes, since it is possible that the olives will never become susceptible to tumah at all. Nevertheless, the modest ones of Beis Hillel were stringent with themselves and acted in accordance with the view of Beis Shammai.