Although all of the holidays are beloved to the Jewish people, it seems that Pesach has a special place in our hearts. For this reason, the Seder is the most widely practiced Jewish home ritual. I would not be surprised if this has its roots very deep in the Jewish collective consciousness the Jewish soul understands that if G-d is said to be closest to us during the High Holidays, we are closest to him at Pesach.
The gemara (Berachot 28b) tells us that Rabbi Eliezer had several parting words of advice to his students, the last of which is seen decorating many parochot, i.e. the statement, dah lifnei mi atah omed, meaning that when a person prays, they should know in front of whom they are standing. I would like to emphasize the first word, dah.
Perhaps one understands, as a result of a philosophical construct, and maybe in English or other western languages that is called knowing. In Hebrew, I would suggest that leda'at is something that needs no proof. It is an intuitive knowledge that is clearer than anything that needs to be understood. Indeed, our own existence is something that a person clearly intuits in this way, making Descartes famous words, cognito ergo sum, superfluous to our ancestors.
Thus, R. Eliezer was telling us to clearly intuit G-d's presence, in the same way as we would intuit the existence of any other interlocutor when we are speaking to them. This is clearly not something that goes without saying our intuitive knowledge is only automatic when dealing with the sensible, meaning that which we perceive with our senses. When it comes to G-d, we can only say that He is sensible when a person is in a state of prophecy.
It is no coincidence that the Shulhan Arukh (Orach Chaim 98:1) speaks about the similarity of a person's state in proper prayer and his state in prophecy. The clear intuitive da'at of G-d's presence that we require for true prayer is something that would place a person in a realm that can best be compared with the clarity experienced by a prophet during prophecy.
So how is the average person, even the not-so-average person, supposed to create this intuitive knowledge of G-d when he starts to pray? Our tradition gives us two avenues that are encapsulated in the words of Friday night kiddush which tells us that Shabbat is a zicharon lemaaseh bereshit and apparently also zecher leyitziat mitzrayim. The average Jew, who is not privy to prophecy, sees G-d in nature through ma'aseh bereshit and in history most pointedly through yitziat mitzrayim.
I would suggest that the weekly and regular presence of Shabbat tells us that seeing G-d through his creation remains the primary avenue by which to recognize him. Just as our calendar is only dotted by historical remembrances, it is sometimes difficult to see G-d in history.
While the first thirty years of the State of Israel allowed many to see G-d in history once again, the more recent past has made it somewhat difficult, though certainly easier than for most of the last two thousand years, to identify His presence in history.
In contrast, Shabbat always takes us back to the same universal G-d of creation, a creation that is appreciable in every breath we take (as is mentioned by the rabbis in Bereishit Rabbah 14:9). The complexity of what is required, both in our bodies and in the atmosphere, to allow us to breathe, is something that has the potential to inspire awe regardless of what else is going on around us. The complexity and order inherent in nature brings us closer to G-d as does its beauty.
In reality, the intuitive response inherent to the aesthetic experience is one shared by all. Even such a committed rationalist as Kant felt forced to give an almost mystical explanation for such an experience, which led others to later criticize his approach to aesthetics as being out of character. But if his critics may have been more consistent, Kant was perhaps more honest in his willingness to accept what his intuition told him was obvious.
After the Jews crossed the Reed Sea and sang shira proclaiming zeh e-li (this is my G-d), they entered into a different level of intuitive knowledge, no longer approximating prophecy, but rather surpassing it. Hence the famous rabbinic statement that even the lowest person at the crossing of the ReedSea saw more than Yechezkel ben Buzi. The Jews who crossed the ReedSea did not have prophecy and yet they saw more than one of the most clairvoyant prophets of our tradition.
The rabbis suggest that whenever the term zeh is used, it refers to something to which someone is pointing. So too, at the ReedSea, it is understood that the Jews were pointing to G-d. G-d's presence was so clear to the Jews, that he was as perceivable as, and perhaps even more than, any physical object to which they could have pointed. At the ReedSea, the Jews were privy to G-d's presence both in history and nature at the same time.
When Pesach becomes a reenactment of the Jews' experience of coming out of Egypt, we feel a proximity to G-d like no other. It is for this reason that we do something that one does not find anywhere else in the Jewish calendar we sing G-d's praises (hallel) at night. Since nighttime is a time of physical darkness, when light and colors disappear from the world outside, we normally save hallel for the daytime, when we are more likely to have clear intuitive knowledge of G-d.
At the seder table, we take great pains not to just commemorate but to re-experience. When we do so, we no longer find ourselves aware of the night outside - we are only aware of G-d, both in history and in nature. At that time we can do nothing else but point to G-d and sing shira.