|The conference center can get a bit loud before the session starts, because everybody's talking to their neighbor. 21,000 people all talking to their neighbor at the same time makes a bit of background noise. Most of the people there wait for as much as an hour and a half for the proceedings to begin, so it isn't very practical to enforce an arbitrary silence.
The amazing thing about LDS adults, however, is how quick they respond to certain cues to be quiet. For example, when a prayer is given, any group will quickly go from being rambunctious to dead silent very quickly. This, of course, does not apply to activities involving children, but children under eight aren't allowed to watch conference live anyway.
Imagine taking the prayer example and multiplying it by the appropriate number to apply it to 21,000 people. Also, add a much better reason to be silent, such as the prophet making his entrance.
In about a second and a half, the congregation went from casually talking with neighors to standing at a dead silent attention. 21,000 people simultaneously stopped doing anything other than breathing. And after about a second and a half, one could have heard a pin drop off the top of the church office building.