It's hard to describe to someone who isn't already using it exactly what Twitter is and how it works. It's sort of a hybrid between LinkedIn (you have a profile and a network of contacts) and a chat room (your tweets are short and can be read by anyone who chooses to "follow" you).
So, how can tweeting get you a job? In Using Twitter for Job Search, Louise Fletcher explains how a job seeker can benefit from Twitter:
1. Connect with recruiters
2. Listen for opportunities
3. Tell people that you need a job
4. Be impressive - add value
5. Communicate well with your Twitter page
Louise has reports of people who won jobs through Twitter. I can't promise the same for you, but I recommend Twitter as one of the many ways you may make your next career move.