The Shema contains the most familiar words in Judaism.
If we want to understand the meaning of the Shema, we can find any number of good commentaries and articles — in print and online.
But if we look closely at the text itself, anyone can see: It’s not a prayer to God at all. In fact, saying the Shema, we’re not even speaking to God. Instead, God is speaking to us!
The first word, “hear,” suggests to us that we should listen closely and think about what we’re being told.
The words of the Shema are also found in the tefillin we put on ourselves, and the mezuzah that we put on our houses.
Why, then, does saying the Shema have such a crucial place in our liturgy (prayer-service)?
To understand this, we have to first know that the Shema was originally said by the kohanim — priests — as part of the Temple sacrificial service, before it later became said by everyone (especially in synagogue services). 
In the Temple, the animal to be sacrificed was first slain and then cut into parts. A whole animal would not have been manageable; parts could be carried to the altar more easily. This was part of the preparation for offering the animal into the altar-fire.
After the animal was slain, but before it was brought to the altar to be burned, the priests recited the Shema  before the animal’s parts were placed in the fire. (That they also recited the 10 Commandments is a topic that I will let pass for now). 
What was the purpose of saying the Shema at this point in the procedure?
Looking at it purely functionally, two possibilities occur to me:
1 — After the animal was slain, time would likely have been required to dismember it, to prepare it to actually be placed on the altar fire. The kohanim/priests who weren’t actively involved in the procedure could only wait. In such situations, it’s very natural for the attention and interest to wander. The Shema served to keep the priests’ attention on the sacrificial procedure during the unavoidable interlude.
2 — The ritual of placing the parts on the fire had to be done with deep thoughtfulness. The Shema served as a meditation for the priests, so that when the time came to place the parts of the animal on the fire, the priests would do it in a devotional frame of mind.
The two possibilities aren’t mutually exclusive. Saying the Shema — and thinking about the import of the words — might have served both purposes simultaneously!
All the comments and commentaries we might read about the Shema focus and deepen our own thinking about both its general meaning and its specific application in our own personal lives.
The Amidah, unlike the Shema, is an actual prayer. It functionally represents (without replacing) the daily burnt offering. As it relates to the synagogue service, based on its place in the Temple avodah (service), we can look on saying the Shema as a meditation in preparation for saying the Amidah.
My point in this post is that saying the Shema serves a cognitive purpose. It’s not just said as an impersonal formality (as is saying the “Pledge of Allegiance” at the beginning of the school day). In the Talmud, the Shema is required to continually remind ourselves that God is the only power over everything; our relationship to this “ultimate super power” is and should be loving; all of our actions have consequences and, finally, that we commit ourselves to follow the directions God gives us. The ideas are reinforced or re-emphasized by repetition. In the liturgy, though, this also prepares us to place all of our needs completely in God’s hands, as we do or are meant to do by doing the Olah Tamid (perpetual daily offering) and saying the Amidah.
Saying the Shema with thoughtful awareness of its implications is meant to bring our attention to God’s Presence, preparing us to then turn our lives entirely over to God in the Amidah.
As Rabbi Dovid Sears wrote:
“I remember reading that Rabbi Dov Ber, the ‘Mittler Rebbe’ of Lubavitch, once said, ‘The deeper one’s ‘Shema,’ the deeper one’s Shemoneh Esreh’ — or something similar. I no longer have the source.” 
The same process is reflected in “Adon Olam,” which I believe is a model of how contemplation leads to prayer that parallels the one in our liturgy itself.
“Adon Olam” begins by stating certain ideas about God: “He reigned, He reigns, He’ll always reign…” The “statement” is being made to ourselves by ourselves through saying the words of the poem.
These ideas remain “abstract” until they are applied personally: “He is my God…”
This leads us to surrender — “Into His hands I place my soul…” — which corresponds to what we are doing by the Tamid — daily sacrifice — and the Amidah.
Even the Amidah itself reflects this same process: The first three blessings — praises of God for “abstract” qualities (e.g. “Your are mighty…Bless You, the mighty God”) — are followed by personal “petitions” expressed as blessings (e.g. asking for health, we say “Heal us…; Bless You Who heals…”).
I have been to eclectic and creative services in which the Shema might be said anywhere during the service. I don’t criticize how others worship. But I suggest that knowing the source of saying the Shema — i.e. the priests in the Temple, before the climax of the daily sacrifice — we can feel clearer about what we’re doing in the synagogue service and why. If we choose to be eclectic or creative, it might also suggest to us ways to use the Shema as a preparatory meditation to the more personal aspects of worship, or for a silent, internal prayer in place of saying the Amidah text.
(For more on this discussion, see:
 See Mishnah Tamid 5:1
 Rabbi Jonathan Sacks points out that the priests’ reciting of the 10 Commandments originally preceded saying the Shema:
“There was a time when there were not three paragraphs in the prayer we call the Shema, but four. [MIshnah Tamid 5:1] tells us that in Temple times the officiating priests would say first the Ten Commandments and then the three paragraphs of the Shema.” See:
Taken together, then, the priests were recalling the Revelation at Sinai and the necessary human reaction to it, before commencing the sacrifice.
(I emailed chabad.org about an actual source. On 5/26/16, I received the following response from Rabbi Yehuda Shurpin: “Not necessarily those exact words, but this is the discussion in his preface to his Sefer Imrei Binah i.e. about the necessity of [saying] Shema before Shemoneh Esrei.”)