How does being a postdoc work?
There are a wide variety of postdocs available, which makes summarization challenging.  Typically, the goal of a postdoctoral fellowship is to broaden your research experience and better prepare you for a career in academia immediately after your graduation with a PhD.  Postdocs are extremely common in the sciences.  (Perhaps they are a bit too common.)  As mentioned by Andreas Blass in the comments, many positions are advertised seeking recent (i.e., within 2-4 years) PhD grads.

It is possible to do multiple postdocs sequentially, though anything beyond two is a bit of a red flag for being hired in academia.  It's probably best to think of your PhD graduation as starting a clock for academic positions.  If you haven't gotten an academic position within five years, then the application process becomes quite different.  If you are planning on waiting this long, you would likely be better off working in industry or at a research lab and attempting to make the transition back to academia without doing a postdoc.  (I'm not familiar with this process, so I won't comment on it.)

If you're interested in more information about postdocs, I can recommend the following sources:


The National Postdoctoral Association has terrible web design, but there's lots of good information there if you can dig for it.
Georgia Tech's Office of Postdoctoral Services has a lot of great information, albeit targeted towards GT Postdocs.  You should also look to see if the places you're applying have a similar organization.
Peter Feibelman's A PhD is Not Enough!: A Guide to Survival in Science is a relatively short book on how to succeed as a postdoc.  It was recently updated, and is probably the best generic introduction to life as a postdoc available.
The CRA's Postdoc Best Practices Guide is intended for postdocs in computing, but I don't see why it wouldn't be valuable to a broader audience.  It's much shorter than Feibelman's book, and covers some of the same ground.