Since a platform is an elevated structure, it is obviously much more prominent than everything around it. Therefore, what happens on it should be of special significance. This is easily understood when one considers the fact that, ubiquitously, a platform is a place from which important or well-known individuals make announcements, conduct affairs, or do presentations for our entertainment.

Because of its conspicuous nature and its ideal natural design, the platform in Lord of the Flies is chosen as the place from which meetings will be conducted. Symbolically, this means that it represents civilized order. It is here where the boys gather to make important decisions and discuss matters of concern. Meetings have rules and these have to be respected. In this sense, then, the platform also becomes a symbol for respect and unity. Irrespective of where they are on the island, the boys go to gather on the platform when a meeting is called. This is where they coalesce as a group.

In addition, once the boys are on the platform, they rise above the ordinary. One can, therefore, also infer another symbolic connotation: the platform uplifts them from their most basic instinct -- their innate savagery -- and forces them to become more humane. They are expected to maintain themselves once they are in a meeting there. In this regard, the platform symbolizes their humanity and the fact that they are supposed to be the superior of anything savage, such as the wild animals on the island.

As soon as the boys stop having meetings and using the platform, they descend into savagery, and a state of anarchy soon ensues. The unity in the group is broken, and the boys split into opposing groups. In the end, almost all humanity is lost and only antipathy remains.

The assembly platform is where Ralph and Piggy originally sat and used the conch to gather the boys from all over the island.  It is where Ralph is voted leader and where he brings the boys to gather when he wants to "govern" - to give duties and chastise and debate about what should be done. 

One had to sit, attracting all eyes to the conch, and drop words like heavy round stones among the little groups that crouched or squatted. 

Thus, the platform represents the seat of government on the island.  Without the platform - no government, anarchy ensues. 

And htis is exactly what happens.  Slowly, the power of the assembly is undermined by Jack, and fewer and fewer boys gather at the platform.  Before the end, it is only Ralph, Piggy, Sam and Eric.  Then the platform - i.e., the government of the island - is attacked by Jack and the hunters, who take Piggy's glasses.  When this happens, all power has shifted to Jack's group and away from the assembly, and this is the beginning of the end - no more civilization on the island.  

In Lord of the Flies, what do the assembly and the killing symbolize?

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.