There is a minhag by some kehillas in chutz L'aretz and by almost all kehillas in Israel to say the complete version of Hallel in the shul during maariv on the first night of Pesach (and second in chutz L'aretz). Where does this minhag come from? Why is this done in those places that do say?
The source is Shulchan Oruch Orach Chayim 487 (4)
בליל ראשון של פסח גומרים את ההלל בצבור בנעימה בברכה תחלה וסוף ובן בליל שני של שני ימים טובים של גליות On the first night of Pesach, we complete the Hallel with the community with a pleasant tune and a blessing at the beginning and end. The same is on the second night outside Israel.
The Rema points out that this is not “our” custom.
mevakeshlev gives several approaches from the Rishonim to explain this practice.
A. In Chazal’s times, there were no siddurim and therefore the common people davened together with the chazzan or by listening to the chazzan’s prayer. (This is why the chazzan is called a shaliach tzibur, the emissary of the community, since he indeed prayed on behalf of many individuals.) On the days that we are required to recite Hallel, these people listened to the chazzan’s Hallel and responded appropriately and thereby fulfilled their mitzvah. However, how could they recite Hallel Seder night? They did so by reciting Hallel together with the chazzan in shul before coming home (see Gra, Orach Chayim 487).
B. A different approach contends that the community recited Hallel in shul the first night of Pesach in order to fulfill the mitzvah with a large group. Although one may recite Hallel by oneself, reciting it communally is a greater observance of the mitzvah.
Neither of these two approaches necessarily assumes that Hallel on Seder night requires a bracha. Indeed, the Chazon Ish recited Hallel in shul Seder night without reciting a bracha beforehand. There are congregations in Bnei Braq that follow this approach.
C. A third approach contends that the primary reason for reciting Hallel in shul is to recite a bracha beforehand. These poskim contend that Hallel at the Seder would require a bracha if it was not interrupted by the meal; to resolve this, Hallel is recited twice, once in shul with a bracha without interruption, and then a second time during the Seder. According to this opinion, Hallel Seder night fulfills two different purposes:
(1) We sing Hallel to Hashem as we do on all Yomim Tovim because of his miracles; on Seder night we sing Hallel at night because that is when we were redeemed.
(2) We praise Hashem while performing the mitzvos of Seder night – haggadah, matzah etc. Although one could fulfill both of these mitzvos by reciting Hallel one time during the Seder, one would miss making a bracha. Therefore, Hallel is recited during davening so that it can be introduced with a bracha, and is sung again during the Seder so that it surrounds the mitzvos of the night. This is the prevalent practice of Sefardim, Chassidim, and the most common approach followed in Eretz Yisroel today (see Gra, Orach Chayim 487).