The Torah (Devarim 15:3) refers to matzah as "lechem oni". The second word, which we pronounce as "oni - answering", is written in the Torah "ani - poor". When interpreted using the written form of the word (i.e. the ksiv - "ani") the phrase means poor man's bread. Shmuel (Pesachim 36a) understands the pronounced version of the word (i.e. the kri - "oni") to be the source that we are to recite many recitations over, and in conjunction with, the matzah. The Talmud further understands "lechem ani - poor man's bread" to prescribe the meager ingredient list of flour and water and to exclude matzah made with wine or oil as well as what we call today egg matzah. In addition, we are taught that just as when an impoverished individual receives a loaf of bread he saves a half for the future, so too the matzah is characterized by it being a prusa - a broken half.
We integrate both themes - oni and ani - at the Pesach Seder. We begin the recitation of magid with "Ha lachma anya", thus highlighting matzah's role as the bread of affliction over which we are going to recite (oni) the Hagadah (specifically, magid and the first two paragraphs of Hallel). Immediately prior to magid we break the middle matzah at yachatz just as a poor man would save part of his loaf of bread in order to present the matzah in its true form following the ksiv - ani. We further integrate the kri and ksiv by proclaiming that the matzah is the bread of the poor, and we invite the poor to join us in our celebration.
The mishna (Pesachim 116b) teaches that in every generation we are to view ourselves as if we personally left Egypt. Rav Yosef Salant zt"l suggests (in Be'er Yosef) that by proclaiming that this is the bread of the poor we relive the evening of the Exodus, reminding ourselves that our ancestors were slaves and poor and ate matzah for centuries prior to the Exodus, helping us focus on that frame of mind, and allowing us to feel as if we personally left Egypt. It is thus understandable that the declaration, "ha lachma anya di achalu avhasana b'ar'ah d'Mitzrayim - this matzah that our ancestors ate in the land of Egypt" has two connotations. The first connotation is that we ate matzah as slaves, and the second is that we ate matzah on the way out of Egypt. It speaks of our servitude and our freedom. Perhaps, then, another reason for splitting the matzah at yachatz is to call attention to the dual theme of matzah and note that the larger half is for the afikomen, the sign of our freedom and deliverance.
The Bear Yosef additionally notes that while there is the mitzvah to invite the poor and needy and those who are alone to all yom tov meals (as the Rambam emphasizes in Hilchos Yom Tov 6:18), the special mitzvah on the night of Pesach to have the needy at your table is a further fulfillment of demonstrating that you personally left Egypt in that very state. It is the actual reliving of the moment. Hence, the inclusion of "kol dichfin yeisei v'yeichol- let all who are hungry and needy join us."
There is one more fascinating connection between the ksiv of ani and kri of oni. The Torah informs us that the Jewish people demonstrated incredible faith by leaving Egypt without provisions. True, we are taught that the Egyptians gave the former slaves silver and gold vessels and garments, however they did not have food except for the matzah they took with them. Rashi (Beshalach 16:1) teaches that miraculously that matzah lasted and sustained them for thirty one days and sixty one meals! By proclaiming and pointing to the matzah, the poor's man bread, we are encouraging the poor that just as He provided for all of us who were needy at that time, may He similarly provide for those still impoverished.
Ha lachma anya thus bespeaks of our historical past, our faith and our optimism.