The second chapter of Massekhet Beitza, which begins on the last daf (15b), focuses on preparations for Shabbat and Yom Tov. The Mishna deals specifically with the case of Yom Tov falling out on Friday, when it is necessary to prepare for Shabbat on a day that has its own restrictions regarding food preparations and other melakhot.
The Gemara on our daf brings a well-known disagreement between Hillel and Shammai. Shammai would prepare for Shabbat every day of the week in the following manner: Each time a delicacy came his way, he would purchase it and set it aside for Shabbat. If he found something better in the course of the week, he would replace the original delicacy with the new-found one, and eat the first one. In that way, his meals – not only on Shabbat, but throughout the week – were eaten with Shabbat in mind. Hillel, on the other hand, did all of his activities for the sake of heaven, quoting the passage in Tehillim (68:20), “Blessed be the Lord, day by day…”
While Shammai’s behavior is fairly easy to understand, Hillel’s demands some explanation.
Rashi explains that Hillel had full faith in God and was certain that He would make sure that all of the food and other Shabbat needs would be made available for him. Thus, he did not spend time and effort preparing for Shabbat on his own. The R”i Abohav explains that all of Hillel’s activities throughout the week were with Shabbat in mind, so there was no need for him to announce that a specific purchase was for Shabbat.
The Hatam Sofer argues that Hillel devoted his entire life to the service of God, so that everything that he did (and not only specific acts of mitzva) was with the intention to fulfill God’s desire. As such, all of his activities – even his apparently mundane weekday activities – were infused with intentions of mitzva.
The general agreement among rishonim and acharonim is that, in this case, it is Shammai who should be emulated, not Hillel. In many places, Shammai’s tradition is quoted as normative and praised (see, for example, Rashi’s commentary to the Torah, Sh’mot 20:8), while Hillel’s is seen as appropriate only for people with a unique level of faith – and inappropriate for the average person.