I think the type of layering you're talking about is overlapping. A simple example would be bookshelves or mantels. Instead of lining things up, they are grouped so that they overlap or partially cover each other. It's much more interesting and natural looking when things offset and enhance each other that way. You can also look at it in terms of how, say, a cream chair is backdropped by blue drapes, maybe just partially, and they play off each other.

Also pay attention to the aesthetics and shapes of the negative/blank space when doing this.

I fall in the more-is-more style of decor so layering is arranging several things on a table or other surface in a harmonious way. For example I might use a runner, a lamp, a plate on a plate stand, a plant, a statue, and a decorative box all together on a buffet or hall table. Or I might use several candles in candlesticks arranged in a group perhaps on a silver tray. Another example is using several pillows of different sizes or shapes on a sofa or bed with some arranged in front of others and a throw as well. One thing I like to do is overlap framed pictures on my mantel. Using an area rug on top of carpet is more extreme layering.

I think layering has to do with embellishing, textures, as well as patterns.

The layered look, while the term may be fairly recent, goes way back. Victorians decorated this way with the layers of window treatments and doilies under every tschotske and ornament.

There are some styles in which layering works better than others I believe. Contemporary style would lend itself to less or even no layering whereas English country cottage, Victorian, even Traditional almost require it.

ok, that's probably more what you're talking about, not overlap : ) You might think of how you layer things when dressing a bed, including the different colors, textures, and patterns. Or layering a skirt over a table, then maybe a piece of glass or lace. The accessories could also be thought of as another layer. Or the layered look in clothing, which I've always loved.

Christopher Lowell talks of his 7 layers of design, which is another way to look at things (linked). He probably has a definition of layering on there, which I had intended to post, but forgot to look!

Here is a link that might be useful: Christopher Lowell - 7 Layers of Design

I think of layering in the Christopher Lowell way - developing a design plan by starting with the permanent elements in the room and moving on to the elements that are more easily changed out. So, with this approach, when you wake up one morning and decide you want to incorporate pink polka-dots in your room, you do it in the throw pillows, not the wall-to-wall carpeting.