OPINIONS: The Mishnah states that a woman who marries a Kohen may eat Terumah only after the Chupah has been performed. The Mishnah and Gemara use the word "Chupah" in a number of places but the Gemara never describes exactly what constitutes "Chupah."
The word "Chupah" appears in Tanach in Yeshayah (4:5) and Yoel (2:16). Its root is the word "Chofeh," or "cover." This implies that "Chupah" refers to something which "covers" the Kalah in some manner. The Radak (in Yoel) is uncertain whether the Chupah of a Kalah is a roofed room, or ornaments with which the Kalah covers herself. What type of covering constitutes the Chupah to which the Mishnah refers, and how does this Chupah effect Nisu'in?
(a) The RAN cites the view of the GE'ONIM (1a of the pages of the Rif; see Insights to 48:2), which many understand is also the opinion of the RAMBAM (Hilchos Ishus 10:1). They maintain that Chupah means that the Chasan secludes himself with the Kalah to the absolute exception of anyone else (Yichud). The Rambam adds that the woman must be Re'uyah l'Bi'ah at the time of the Chupah.
According to this view, it seems that Chupah accomplishes Nisu'in the same way that Bi'ah accomplishes Nisu'in -- it is the beginning of an intimate relationship of Ishus. (TOSFOS to Yoma 13b, DH l'Chada, seems to accept this understanding of Chupah with regard to an Almanah, but not with regard to a Besulah.)
According to the Ge'onim, the word "Chupah" might mean that after this display of intimacy the husband feels responsible to be his wife's protector who "covers" or shields her. This is the way the Perishah (EH 61:2) interprets the word "Chupah."
(b) There are many proof against this opinion (as discussed earlier in Insights to 48:2). It seems that the Rambam himself does not require an actual act of Yichud that is Ra'uy l'Bi'ah. Rather, Chupah means that the woman is brought into the husband's house "l'Shem Nisu'in," for the purpose of Nisu'in, in a semi-private manner. (That is, they may be still visible to others who watch them from the outside.) This is the way the BEIS ME'IR (EH 55:1) explains the opinion of the Rambam, and the MAGID MISHNEH (end of Ishus 10:6) seems to interpret the Rambam this way as well. (See also BEIS SHMUEL EH 57:2 and BACH EH 61.)
The RAN (see also VILNA GA'ON EH 55:9) also defines Chupah as "bringing the Kalah into the Chasan's house l'Shem Ishus" (and he does not seem to require any type of Yichud). The Ran adds that the source for this Kinyan in the Torah is the verse in the Parshah of Hafaras Nedarim, "v'Im Beis Ishah Nadarah" (Bamidbar 30:11), which describes the married woman as "in the house of her husband." The TUR (EH 61) defines Chupah as Yichud (but he apparently does not require that the Kalah be brought into the Chasan's house; see DERISHAH 61:1 and PERISHAH 61:2).
The Rambam, Ran, and Tur all seem to define Chupah in a similar, if not identical, manner. According to their understanding, the "covering" of Chupah might mean that the Chasan covers the Kalah with his home -- he brings her into the shelter of the roof of his home.
(c) Others explain that Chupah is a symbolic act which shows that the Chasan has designated the Kalah for himself and is about to bring her into his home permanently to be his wife. This act could be an act of covering the Kalah ("Chofeh") in some way.
The TASHBETZ (Tashbetz Katan #461) and the REMA (EH 55:1) describe Chupah as a cloth or curtain spread over the heads of the Chasan and Kalah. This is what is commonly called Chupah today. This canopy might also allude to Kabalas ha'Torah, where Hash-m "married" the Jewish people by holding the mountain over the people in an act of "Chupah." (In fact, the Tashbetz (#465) writes that "all of the customs of the Chasan and Kalah are learned from the giving of the Torah, where Hash-m appeared to us like a Chasan coming to greet the Kalah, the Jewish people." See Rashi to Shemos 19:17.)
The ME'IRI (Kesuvos 7b) writes that the practice at one time was to take a corner of the head covering of the Kalah and cover the Chasan's head with it. The YAM SHEL SHLOMO (Kesuvos 1:17) writes that they covered the Kalah's head with the Chasan's Talis. (An allusion to this is found in the Gemara in Kidushin (18b) which refers to marriage as "spreading one's Talis" over one's wife.) This practice is also alluded to in the verse in Ruth (3:9) which relates Ruth's request of Boaz that he "spread his garment over your maidservant."
TOSFOS in Yoma (13b) writes that covering the Kalah's head with the veil ("Hinuma") constitutes Chupah (at least for a Besulah). The Hinuma is a sign that she is now a married woman. An allusion to this may be found in the verse that relates that when Rivka saw Yitzchak for the first time as she was brought to him to marry him, she covered her face with a veil (Bereishis 24:65).
(The BA'AL HA'ITUR (Birchas Chasanim, #2) writes that Chupah means the Chasan's act of bringing the Kalah into his home, or an adorned bridal canopy, after he has decorated it in her honor. The Ba'al ha'Itur apparently follows the view that Chupah is a symbolic act which shows that the Chasan is about to take the Kalah into his home permanently as his wife.)
HALACHAH: Nowadays the custom is to fulfill most of these opinions of Chupah at every wedding, as the BACH (EH 61) writes. The Chasan lowers the veil over and covers the Kalah's face ("Badeken"), which is the Chupah according to Tosfos. They stand underneath a canopy that is spread out over the two of them. The Chasan then brings the Kalah to the Yichud room, where they eat together in a private place (REMA EH 55:1).
The Poskim (ARUCH HA'SHULCHAN 55:18) mention that according to those who maintain that the Chupah constitutes bringing the Kalah into the Chasan's house, the Chasan should buy (or rent) the Cheder Yichud so that the area into which he brings the Kalah belongs to him. (However, the VILNA GA'ON (EH 55:9) maintains that it is not necessary for the Chasan to own the land where they are standing in order for the Chupah to take effect.)