1) The Gemara here (64b) explains that the reason it was done by many Kohanim is because "in the mulititude of people is the King's glory" (Mishei 14:28).

(I do not know why seven Kohanim did not each light one candle of the Menorah.)

2) It seems that the lines of Kohanim are mentioned only in connection with the Korban Pesach. It may be that the reason is because this was the only time in the year that so many people were all bringing the same kind of Korban. If it would have been done with other Korbanos, the Kohanim could get confused which type of Korban they were passing the blood along for. One Kohen would think it was for Korban A, and another Kohen would think it was for Korban B, and there would be a mix-up concerning the Kavanah Lishmah (and thus the validity) of the Korbanos.

3) I found, bs'd, that the Machatzis ha'Shekel on the Magen Avraham (147:11) gives an additional reason for the lines of Kohanim. He writes (quite near the beginning of #11) that on Erev Pesach there were lots of Pesach offerings brought, and crowds of people in the courtyard of the Beis ha'Mikdash, so there was not much space to walk around the Azarah. The Machatzis ha'Shekel adds that the main reason for the lines was "b'Rov Am Hadras Melech" as we mentioned above, from the Gemara on 64b; but nevertheless we learn from the Machatzis ha'Shekel that the crowding aspect in the Beis ha'Mikdash was also a factor involved in Chazal saying that the Holachah should be done by the line of Kohanim.

I arrived at this Machatzis ha'Shekel through a Sefer called "v'Nakriv Lefanecha b'Ahavah," published by "Machon l'Dvir Beisecha" (Lakewood, NJ), page 42 and note 346. He writes in the name of the Machatzis ha'Shekel that because of the crowds in the Beis ha'Mikdash which made it difficult to walk to the Mizbe'ach in order to pour on the blood, they did the sprinkling of the blood in this more orderly way so that things should not be disorganized.

All this would apply only on Erev Pesach when there were such great crowds in the Beis ha'Mikdash.

4) The Sefas Emes suggests that says that one could say that the reason the blood was passed along was so that it would all get finished more quickly, since walking along is slower than passing. However, the Sefas Emes then writes that the Rambam explains that the reason for this is so that everyone should have a part in the Mitzvah, and this is what the Gemara here means when it says "b'Rov Am Hadras Melech."

The Rambam is in Hilchos Korban Pesach (1:14) where he writes that each Kohen passed it on to his friend "so that many will occupy themselves with this Mitzvah." We learn that according to the Rambam, this concept is identical to "b'Rov Am Hadras Melech," which is mentioned in the Gemara. One sees that "b'Rov Am Hadras Melech" does not mean that for the onlookers it is the honor of Hash-m that many people do the Mitzvah. Rather, the stress is not on the onlookers but rather on the people doing the Mitzvah. Chazal want as many people as possible to be involved in the Mitzvos.

5) This is especially relevant to Pesach, which is the "Festival of Participation." Just as the whole of the Jewish people left Mitzrayim on the night of 15 Nisan, so we have to try and feel every year that we are coming out of Mitzrayim right now. The more Jews who participate and enjoy the Seder nights, the greater is the honor of Hash-m.

6) Let us discuss the source for "b'Rov Am Hadras Melech" in the Torah:

a) I am digressing a little, but I think it is worth mentioning that it seems to me that we learn from this Sugya a big Chidush -- namely, that it appears that there is a source in the Torah for the concept of b'Rov Am Hadras Melech. This is surprising, since b'Rov Am Hadras Melech is a verse in Mishlei 14:28, so one would probably have described it as "mi'Divrei Kabalah" which is usually the way we describe Halachos that we derive from Nevi'im or Kesuvim and, generally speaking, possess less authority than a d'Oraisa.

b) My source for this suggestion starts with the Rambam that I cited above. The Rambam writes, "So that many will occupy themselves with this Mitzvah." Now, in the Gemara it says b'Rov Am Hadras Melech, so we see that the Rambam learns that b'Rov Am Hadras Melech means that many people do the Mitzvah. This reminded me of what Rashi writes (Vayikra 26:8) when commenting on the Torah's statement that when we follow the will of Hash-m and fulfill the Mitzvos, five of us will successfully pursue 100 enemies, and 100 will successfully pursue 10,000. Rashi points out that the proportions are not equal; it should have said that 100 will pursue 2,000. Rashi answers that we learn from here that there is a difference between a few people who keep the Torah and a lot of people who keep the Torah. We learn from Rashi that there is a special spiritual strength in large numbers of people who do what the Torah wants. Now that we have suggested that there is a source for B'Rov Am in a Torah verse, we may be able to understand a little better why B'Rov Am is mentioned in quite a few places in Shas.

7) The above was a digression but I want now to try to add a little bit of understanding to the Machatzis ha'Shekel that I cited in my second answer. He stresses that the chief reason for the lines of Kohanim was B'Rov Am as stated in the Gemara. However, he also adds the practical reasons. If every Kohen would take the blood on his own to the Mizbe'ach, there would be an awful lot of accidents. The Azarah was so crowded on Erev Pesach that Kohanim would be colliding with each other all the time, and blood would frequently be spilled on the floor. To avoid this scenario, Chazal said that the Kohanim should be in organized lines and now there will be no collisions. But why does the Machatzis ha'Shekel give us these practical reasons if the Gemara states explicitly that it is because of B'Rov Am? I think the answer is that we always try to fulfil B'Rov Am if we possibly can, but on the other hand one has do this in a way that will be acceptable to the Kohanim. For instance, if -- on every weekday -- we would light the seven candles of the Menorah through seven different Kohanim, they would quickly find this tiresome and would not want to continue. Instead, Chazal waited for the busiest day in the year in the Beis ha'Mikdash -- Erev Pesach -- and instituted this system of taking the blood to the Mizbe'ach using the lines of Kohanim. Chazal used their wisdom to take advantage of the incredible crowds in the Beis ha'Mikdash, in order to introduce a technique which involved the very important idea of B'Rov Am Hadras Melech.

8) I found that the Mesivta edition of the Gemara cites one of the Rishonm, the Or Zaru'a, who compares our Mishnah with the Mishnah in Tamid 4:1. Our Mishnah states, "The Yisrael slaughtered the animal and the Kohen received the blood." The Mishnah in Tamid states, "The slaughterer slaughtered the animal and the receiver received the blood." But our Mishnah continues and describes how the blood was passed on from one Kohen to the next while the Mishnah in Tamid says nothing about that.

The Or Zaru'a (1:125 DH Ashreichem) writes that the difference is that many people were anyway busy with the Korban Tamid and Hadras Melech was fulfilled without the need for the line of Kohanim.

Dovid Bloom