The passage comes to explain that we broke the matzah at Yachatz in order to commemorate how the Children of Israel hastily broke and shared their matzah with each other on the night of the Exodus.
Relationship between the lines – According to this commentary, the first two sentences explain that we split the matzah exactly as the Israelites did on the eve of their departure from Egypt when, in their haste,2 they divided and shared it with whomever had not yet prepared any. The second and third lines thus reenact the nation's words in Egypt, as they offered to share their Matzah and Paschal sacrifice with all and expressed their hopes to be free people in Israel by the next year.3
"לַחְמָא עַנְיָא" – This approach understands "לֶחֶם עֹנִי" in the verse in Devarim 16 and "לַחְמָא עַנְיָא" in the Haggadah to refer to the broken bread which a poor person eats. While a similar interpretation is recorded already in Bavli PesachimPesachim 115b-116aAbout the Bavli, the Commentary attributed to Rashbam differs in explaining that the Israelites ate this broken bread due to their haste, rather than because they were poor. Accordingly, the commandment to eat "לֶחֶם עֹנִי" is elucidated by the continuation of the verse "כִּי בְחִפָּזוֹן יָצָאתָ מֵאֶרֶץ מִצְרַיִם".
"דִי אֲכָלוּ אַבְהָתָנָא בְּאַרְעָא דְמִצְרָיִם" – when? This refers to the matzah that our forefathers ate on their way out of Egypt, rather than to the food they ate during their slavery.4
"כָּל דִּצְרִיךְ יֵיתֵי וְיִפְסַח" – The word "וְיִפְסַח" describes the partaking in the Paschal sacrifice offered in Egypt.5
Why in Aramaic? The "Rashbam" Commentary does not address this issue. If much of the passage is supposed to represent the words of the Israelites themselves in Egypt, it is strange that specifically this section would be written in Aramaic rather than Hebrew or Egyptian. It is possible, though, that the language simply reflects that the passage was first added to the Haggadah only in Babylonia, where Aramaic was the vernacular.6
When do we pour the second cup? This approach might maintain that we pour the second cup after this passage, since it is only then that the Maggid section begins.7
Prelude to Maggid
This paragraph introduces the retelling of the story of the Exodus and is intended to stimulate the children to ask why we eat Matzah.
Relationship between the lines – The Tashbetz explains that first sentence explains that we eat matzah to commemorate the conditions of our ancestors when they were enslaved. The second line then contrasts the impoverished state in Egypt with our current ability to invite others who are lacking to share in our meal.8 Finally, the last line expresses our hope for a full future redemption so that we will be able to then invite others to share in our Paschal Sacrifice as well.9
"לַחְמָא עַנְיָא" – According to the Tashbetz, "לֶחֶם עֹנִי" describes the physical properties of the Matzah.10
"דִי אֲכָלוּ אַבְהָתָנָא בְּאַרְעָא דְמִצְרָיִם" – when? According to this opinion, the phrase refers to the Matzah eaten during the Egyptian bondage,11 rather than to the matzah which accompanied the Pesach sacrifice on the eve of the redemption.
"כָּל דִּצְרִיךְ יֵיתֵי וְיִפְסַח" – The Tashbetz interprets this as a wish referring to the future Paschal Sacrifice which will hopefully be brought in the coming year. Raavan, though, understands "וְיִפְסַח" to refer to the eating of the Afikoman which commemorates the Paschal Sacrifice.12
Why in Aramaic? Raavan and the Tashbetz explain that the short preface was aimed at the less knowledgeable participants who were likely to understand only the vernacular.13
When do we pour the second cup? According to the Tashbetz, as Ha Lachma Anya is an introduction to and part of Maggid, the cup is poured before reciting it.14 However, according to Raavan, the second cup is poured only afterwards, at the beginning of the main corpus of Maggid.15
Independent Unit
The passage stands on its own, and is not integrally related to either Yachatz or Maggid. The approach subdivides regarding the specific purpose of the unit, with some viewing the passage as a reference to the celebration of the Pesach in Temple times, and others viewing the lines as stage directions for the Seder leader.
Commemoration of Temple Times
This passage, at the beginning of the Seder, alludes to the way Pesach was celebrated in Temple times and expresses hope that it will soon, once again, be commemorated in the same way.
Relationship between the lines – The first two sentences represent what a person offering the Pesach in the Mikdash would say as he invited others to join him in the sacrifice.16 He would make reference to the matzah to be eaten in commemoration of our ancestors in Egypt and invite others to partake of the Pesach lamb.17 The last line of the passage, though, represents the words of the present head of household who, living in exile, expresses his sorrow that he can no longer bring a sacrifice in the Temple and wishes that next year he will be in Jerusalem.
"דִי אֲכָלוּ אַבְהָתָנָא בְּאַרְעָא דְמִצְרָיִם" – when? The person bringing the Pesach offering refers back to the matzah eaten by our ancestors with their Pesach.
"כָּל דִּצְרִיךְ יֵיתֵי וְיִפְסַח" – This refers to the Pesach offering brought in the time of the Mikdash. Before Pesach, a person would invite others to join in his group to bring the offering.
Why in Aramaic? This passage reflects the reality of those living in exile post the destruction, no longer able to bring sacrifices. As such, it was likely written in Bavel and is said in the language of exile.
Invitation – Abarbanel views all three lines as part of an invitation from the Seder leader to any needy who want to join the Pesach celebration. He explains that in order not to embarrass the poor, the leader begins by pointing to the poor bread eaten by our ancestors, as if to say, you are not alone in your poverty; our ancestors too ate just matzah. Afterwards he actively invites them to join. The leader ends by pointing out that though he has mentioned the "Pesach", due to the exile they cannot actually offer the sacrifice, but hopefully next year they will do so in Jerusalem.
Distinct directions – R. Y. Reifman suggests that really there is no connection between the lines because they were not originally meant to be said together. The first line accompanied "Yachatz" and represents the words spoken when breaking the matzah.19 The second line was said at the start of the meal, when the Seder leader invited others to join. Finally the last line was originally said at the very end of the Seder, where we now say "next year in Jerusalem" and played a similar role. There are no textual witnesses, however, which support such a hypothesis.
Why here? If this is an invitation, one must wonder why it is first being proffered now, rather than before Kadesh or at Shulchan Orekh. Abarbanel suggests that the invitation comes here since this would normally be where one begins the meal. The leader acts as if he is about to eat, breaking bread (Yachatz) and offering an invitation, but instead stops to tell the story, so as to arouse the curiosity of the children.
"לַחְמָא עַנְיָא" – Abarbanel understands this to be bread fitting for one who is poor, as was eaten by the Israelites in Egypt, and as poor men eat even in contemporary times.
"דִי אֲכָלוּ אַבְהָתָנָא בְּאַרְעָא דְמִצְרָיִם" – when? This refers not to the matzah eaten during the redemption but that eaten while they were impoverished slaves.
"כָּל דִּצְרִיךְ יֵיתֵי וְיִפְסַח" – According to Abarbanel, this refers to the Afikoman which is in memory of the Pesach, rather than to the Pesach itself, which was no longer brought when the passage was written.
Why in Aramaic? Since these lines are not really part of the story but rather instructions for the leader, it is natural that they are said in the vernacular. Abarbanel adds that if this is an invitation, it needs to be understood by its primary audience, the needy, who would not have known Hebrew.