The basic principle is that if you have a classroom without soundfield, the teacher needs to raise their voice to make sure they're being heard throughout the classroom. That means they're straining their voice potentially. And as Graham was saying, the distance sound has to travel across the room means that the clarity of sound deteriorates and the children at the back will not hear as well as the children sitting at the front. It's a very straightforward principle.
If you have a soundfield system installed and working well, it means that the teacher can speak at a normal level. It's also the case that if you're speaking at a more conversational level your voice goes up and down in a natural singsong way. It's a much more interesting sound to listen to. If you have to raise your voice, you're speaking in more of a monotone all the time, which is less pleasant to listen to and it's not so easy to concentrate.