Asides is usually a short post, a few lines, and sometimes shown in the sidebar instead of in the main post area. Over at WordPress they define it in Adding Asides like this:

When you lean towards someone and tell them a little bit of information, you are making an “aside” comment. In blogs, you can do that on your blog by passing on small bits of information to your readers called Asides.

I intend to use Asides as a category with a somewhat different layout but still in the main post area. For me it is more a way to open up for short posts without feeling guilty.