<p>Maybe this is a silly question, but I've always assumed each number delineated by a period represented a single component of the software. If that's true, do they ever represent something different?  I'd like to start assigning versions to the different builds of my software, but I'm not really sure how it should be structured.  My software has five distinct components.</p>

It can be very arbitrary, and differs from product to product. For example, with the Ubuntu distribution, 8.04 refers to 2008.April
Typically the left most (major) numbers indicate a major release, and the further you go to the right, the smaller the change involved.