From R. Daniel Z. Feldman, on YUTorah.org (Pesachim 6a, no link available):
The Talmud (Pesachim 6a) states that thirty days before Pesach we are to “inquire and expound” (shoalin v’dorshin) the laws of Pesach, just as Moshe stood on Pesach and taught about Pesach sheni, one month later. Elsewhere, however, the Talmud (Megilah 32a) refers to such inquiry on the festival day itself (hilkhot chag b’chag, etc.) [BASED ON LEV. 23:1, IN THIS WEEK'S PARASHAH -- GS]. The Ran and the Ritva, in reconciling the two sources, suggest that the thirty day period does not represent a span in which expounding is obligatory, but rather one in which the topic is considered timely, so that a student who asks his rebbe a question in this area is considered “shoel k’inyan”, asking of the topic at hand, even if the rebbe is teaching different subject matter, and thus deserves prioritized attention. (See Taz, 429:1, for an interesting application of this point in the realm of monetary law.)I saw that R. Yitzchak Hutner (Pachad Yitzchak: Sefer Zikaron, I think around p. 249) explains differently. R. Yisrael Salanter (Or Yisrael, ch. 31) differentiates between a chok, a mitzvah whose reason we do not understand, and a mishpat, a mitzvah whose reason we understand. He suggests that learning Torah is always a mishpat because we need to know how to fulfill the mitzvos; even learning about a chok is a mishpat because, regardless of why we have to do the mitzvah, we know that we must learn about it to be able to perform it. (Learning about a mitzvah that one cannot put into practice, such as ben sorer u-moreh, is a chok.) Based on this, R. Hutner suggests that learning about a holiday 30 days in advance is a mishpat, because we have to know how to observe the holiday. But after 30 days of learning the laws, learning about them on the holiday itself is a fulfillment of the learning as a chok, because we already know how to observe.
The extent to which this period prior to the festival becomes an active part of the observance is emphasized by a query posed by R. Shlomo Kluger (Resp. HaElef Likha Shlomo, #384). He discusses a situation where two questioners simultaneously approach the Rabbi on Purim: one with a question concerning Purim, and one with a Pesach question. Which question should be answered first? He leaves the question unresolved; while one might think Purim issues would be prioritized, as it is Purim at the moment, the fact that it is also thirty days before Pesach (see Pri Chadash 421:1) makes Pesach a current reality as well.
Many other Rishonim, however, understand there to be an active obligation to expound the day from thirty days before. This leaves the question, then, as to how to reconcile the two passages. In the understanding of some commentaries (see Bach and Gra to O.C. 601) the fundamental rule is expounding on the day itself, but that obligation expands to begin a month earlier.
R. Chaim Aharon Turtzin (Kuntres Chanukah U’Megilah, Megilah #3) suggests that the two concepts are actually fundamentally different. The obligation that begins a month prior is for the purpose of knowing the relevant laws of the festival, and is structured as such. (See Mishnah Berurah for a discussion of the possibility that the period is shortened for less complicated festivals).The obligation on the festival itself, by contrast, is more of a homiletic nature, to publicize and underscore the theme of the day. Similarly, as R. Yitzchak Sorotzkin observes (Gevurot Yitzchak, Purim, 25) the Kr’iat HaTorah on the festival becomes a fulfillment of that second aspect.