Lord of the Flies is a symbolic novel, so you're right to assume there is symbolic meaning to the people and events of the story. By assembly, I assume you mean the initial meeting on the beach the morning after the boys have landed on the island. This is a time of relative innocence, when the boys were still interested, at least a little, in being civilized and following some basic rules of civilization. They gather, they listen, they vote, and they decide. This meeting is not particularly formal or structured, but it is civilized. In contrast is the episode in which Simon is killed. Here most of the boys have abandoned all semblance of civilization. They have become hunters and savages, and they have certainly given themselves over to their baser (darker, more sinful) natures by this point in the novel. It's a picture of how far they've come in their depravity. The boys are so consumed with hunting and killing on this stormy night that when Simon--one of them--enters the circle all they see is prey. This foreshadows even worse hunting to come, of course.
The assembly seems to symbolize the problems with the political world. At one assembly, we see the hunters tell their tale of the beast, which really doesn't seem to exist, but everyone believes their tale and they are frightened. This particular meeting might symbolize how politicians use scare tactics to persuade voters to support them over a threat that isn't real.
At another assembly, we see Jack twist Ralph's words and accuse Ralph of calling the hunters cowards. Jack then takes the opportunity to storm off with his following of supporters. Politicians also frequently twist their opponent's words.