It's really a very simple system with 2 primary features:
1) Promoted Account- Twitter will recommend your account to people they think might "Follow" you
2) Promoted Tweets- Twitter will display your tweet to people that they think will click on it
What I love about the system is that you are only charged when someone follows you or clicks on your tweet. It works like Google Adwords or Facebook Ads where it is a bidding system and has some sort of algorithm valuing posts and accounts as to how often to display them.
So far I've spent about $40 and had about 17K impressions with over 500 clicks on tweets and for 68 cents have 5 new followers. I'm pleased with these numbers and know that they will change as the bidding will become more competitive as more people use it, but the ads will become more effective as I better develop them and focus the posts.
One key to always remember is that Advertising only speeds up your growth process. If you are irrelevant, ads won't make you relevant or really grow your community at all. You might have some short-term numbers increase, but long-term you will see no change. If you have a growing Twitter following, these ads can really help you grow faster and reach further.
Have you tried using Twitter Ads? Do you think this will hurt or help Twitter long-term?