Layering in electronic music is actually where you play multiple instruments in unison (such as layers of multiple synths), to create a combined fat sound that spans many frequencies.
I'd call it build up, or progression. Just not layering, because that's a reserved term.
If you have a beat and have an instrument play off-beat, I have no idea if that is called something else. That is just part of the harmony because the melody is the dominating sound, anything else that is part of harmony.
I mean, it's sort of like you keep adding more and more instruments untill there are tons of them. It's not just two, with some singer. I guess so. Xadrea thinks it's 'layering.'
Layering is from what I understand is when you are electronically making a sound. In an orchestral setting it's different.
How orchestral music works is that everyone had a different part. You either play melody and harmony. Within the melody and the harmony the parts are different. Sometimes instruments come in at different points in a song. If you are directly looking at sheet music of a song and compare the different sections, say like violin and cello, it will look totally different. A group of instruments may be playing while another section of the orchestra just have a series of rests. Now if there is a word for it, I can't think of it.
Really the better example of this I can think of on the top of my head that you are talking about is The Hall of the Mountain King by Edvard Grieg. [link] That is the best recording I could find but I've heard better. I played it, somewhat of a difficult song to play because not only does everyone kind of step in a moment and step out, but it starts increasing in tempo and getting louder.
Example: "Dark Eyes," by Stan Kenton