In short...it is possible.
Its not as easy as most people lead on though. Its not a case of quit your job, and start blogging instead. Really you need to be an active blogger and start earning before you even think about quitting your day job.
Income can be through a wide range of methods, but it is typically through Adsense (if your blog gets thousands of hits) or through product referral schemes. Both methods rely on your blog having a good amount of traffic...and that doesn't come overnight.
If you are interested in doing it, then I would suggest starting your own website/blog and seeing how you get on. The main hurdle is attracting 1000s of visitors to the site. I would not quit your day job before you are earning a decent income from it, and you have the confidence you could do it full time.