Ask HN: How to use Twitter as a marketing tool?

My boss asked me to run a Twitter feed with links leading to our blog posts about problems our software solves, but I have never used Twitter before, even privately. Honestly speaking I don't get why would people use Twitter in the first place and what is the social dynamics behind it. How come could it generate more incoming links, visitors and eventually increase sales?

Do you know any resources, newbie guidelines about using Twitter as a marketing tool?

How do you use Twitter to generate traffic? Are there certain business areas/subjects that Twitter is more suitable for and other where Twitter should not be employed? What can be done wrong or go wrong with this medium?

Thanks in advace for your answers!