The central part of the Haggadah is from the passukim Devarim 26:1-10 in this week's parasha Ki Tavo. It is the "most concise description in the Torah of the enslavement-Exodus drama." One would have thought that the fuller narrative from Shemos would have been a better choice. There is much discussion in midrash on why these specific passukim are utilized and and, on the level of pshat, what is the simple translation of ambiguous phrase "Arami oved Avi". Avakesh wrote about it here.
Here are some sources that take up these themes.
From a deeper perspective of PARDES, these passages reveal profound truths and we will briefly examine, almost in an outline form, the non-literal explanations from various dynasties of Chassidic thought.
The Tiferes Shmuel (Alexander) states that the the descent into Egypt reflects the destruction (Oved) of the relationship between the Jewish people who are like sons to HaShem, their Father (Avi).
The Ma'or V'Shemesh questions how Lavan was involved in the Jews going down to Egypt and goes further back to the source of all conflicts (especially in the case of food/crops i.e. the bikkurim): the story of Adam (the first father) and the Nachash [In fact, this is the original episode in time for all historical conflicts according to Kabbala] in terms of the pursuit of materialism (gashmiyus) in life. [As an aside, the Koznitzer Maggid in Avodas Yisroel quotes the Shelah (and this is also in the Megale Amukos) and states that indeed Lavan was present in Egypt as Bilaam!]
Breslov sefarim [Likutei Moharan 19 and Likutei Halachos in several places] translate the phrase "Arami oved Avi" that the Aramaic language aka Targum and thus worldly thought (as opposed to Lashon HaKodesh and Torah) destroys a person's thought (which is his father as it is the source for his emotions and actions). The motif of 'fatehr" as the sefira of chochma is identified with the first generation of thought or conception.
The Ishbitzer sefarim (the Mei Shiloach as expanded upon by his grandson the Radziner in his sefarim entitled Sod Yesharim) also discuss that the level of “father” in a person is his thought and will. Therefore the enounter with Lavan was a descent into the world of trickery as further exemplified by the episode with the terafim. One encounters deception in the world where many motivations are hidden. Lavan is white al pi Kabalah since it contains the other colors hidden within. On the journey toward Shavuot, one grows in recognition of the Creator paralleling the life of Avraham Avinu and offers Bikkurim on Shavuot to mark attaining this level in avodah.
Chabad sefarim (Mittler Rebbe and Rebbe Maharash in Toras Shmuel) do not delve deeply into details but also note that "Arami Oved Avi" is a spiritual level which is the anithesis of the holy source for chochmah aka the source for thought which is sync with the previous two definitions.
The Cassidic approaches show us how the farmer's acknowledgement of HaShem's role in his work in the field culiminating with his bringing of Bikkurim to the Temple serves as the mashal to model the spiritual growth of the Jewish people on their elevation from Egypt. "Arami oved Avi" represents the negative barrier rooted in the spiritual worlds that must be overcome in this avodah in order to experience true revelation of HaShem in one's life.