Before receiving the Torah (at the very point in time when Am Yisroel was about to accept the yoke of Heaven for the very first time) Hashem tells Am Yisroel that they are to become a "Kingdom of Priests and a Holy Nation". As astutely pointed out in the #dafchat:
This is indeed hinted at in the first two mishnayos.
However I think that the message goes even deeper. There are many moments in our daily routine where we actually try to perform acts in a similar fashion to the Kohanim. This starts with washing our hands when we wake which according to the Rashba is reminiscent of the Kohanim preparing to do the Avoda:
ולפיכך אנו צריכין להתקדש בקדושתו וליטול ידינו מן הכלי ככהן שמקדש ידיו מן הכיור קודם עבודתו
שו"ת הרשב"א חלק א סימן קצא-
It continues with a number of Halachos brought in the Tur comparing us while we pray to a Kohen while doing the Avoda:
ומעומד דומיא דעבודה דכתיב לעמוד לשרת, והשוואת הרגלים ככוהנים בשעת העבודה... וראוי לו שיהיו לו מלבושים נאים ומיוחדים לתפילה כגון בגדי כהונה" -טור או"ח סימן צ"ח
A third example is Friday night when every father blesses his children with the blessing of Bircas Kohanim. (I used to have more examples, but seem to have misplaced my list. Contributions from readers in the comments are welcome!)
The Mishna is thus implying that when we say the Shema and accept the yoke of Heaven we should once again picture ourselves as Kohanim entering to eat Terumah. Why eating Terumah? (and why indeed so many examples of eating as @TechRav asked?)
This example of eating Terumah concisely summarizes our job in this world - to impart even onto the most simple and mundane tasks an element of Kedusha. All of our interactions in this world can and should be elevated to a status of holiness through our actions and intentions. This is the ideal to which we must aspire.
But there is a danger when we all consider ourselves Kohanim. This is the trap that Korach fell into when he claimed "the whole nation is holy!". Korach was unable to distinguish between techeiles and lavan (as according to the medrash he and his followers wore garments of only techeiles). He could not see that each person has a specific task and falls onto a specific shade within the spectrum. He did not differentiate between the ideal (tachlis) and the practical implementation.
So as the night comes to an end our time of contemplation and dreaming about our place in the world is superseded by our need to get up, act, and implement these ideals in the real world. At this point, when we begin to distinguish between techeiles and lavan, we must once again say the Shema this time focusing on our own unique specific day-to-day tasks.
These two ideas, of finding Kedusha in this world, while each person finds their own place on the spectrum are both in sync with the opinion of Beis Hillel in Mishna Gimmel. As expressed in their words: "Every person recites Shema as he is, and he may do so in whatever position is most comfortable for him". This statement contains both of these sentiments. On the one hand it clearly outlines the need for each person to find his/her own unique expression. On the other it underlines the fact that even when engaging in Holy tasks and pursuits, they should feel natural, as it is indeed the goal to bring these Holy elements even into our mundane world. (As pointed out by I. Knohl ['A Parasha Concerned with Accepting the Kingdom of Heaven', Tarbiz, 53 (1983), pp. 11-32 (Heb.) and Rabbi Y. Nagen [Nishmat Hamishna http://www.daat.ac.il/daat/vl/yakov-negen/yakov-negen01.pdf] this is very much in line with Beis Hillel's general approach especially as seen in Avos De'rabbi Nosson where Hillel Hazaken declares taking care of one's hygiene to be a Mitzva. [see also http://thinkingdafyomi.com/the-law-and-the-spirit-berakhot-11/]
Finally we get to Mishna Dalet which introduces us to the world of Berachos. Brachos (blessings) are one of our most powerful tools which can be used exactly for the purpose of bringing sanctity into mundane activities. Instead of just sitting down to eat we first make a Beracha contemplating from where we got the food, giving thanks to Hashem and thus elevating the entire experience. In juxtaposition with the previous mishna, this one dictates very strict precise rules regarding the Beracha. Everyone agrees that when it comes attention must be paid even to the smallest of details.
This encapsulates our mission from the moment of Yetzias Mitzrayim when we were given this task, and until the Yemos ha'moshiach, at last connecting us to Mishna Hei. (there is room for some improvements regarding the framework, and I'm open suggestions from the audience.)
To sum it all up, one of the hidden lessons of the first perek:
- As we say the Shema we should be aware of our mission to bring Kedusha into this world.
- We must realize this on the ideal level (night),
- as well as the practical level (day).
- Each person has their own unique part in this mission,
- All the time being careful and sticking to the formula, especially when applying the powerful tool of Berachos.