In a nutshell it's informing a publisher of a broken link and suggesting a link of your own to replace it. Check out the Link Building Library [webmasterworld.com], there is a discussion about broken link building there that goes into detail, as well as many other posts about the fundamentals of link building.
As far as it being beneficial or harmful, if done incorrectly it can be not useful at best and harmful at worst. There are ways of doing it that can cause a lot of problems. So if you're new to SEO then maybe you need to back up and get to know the fundamentals before proceeding.
I believe that broken linkbuilding is still a viable strategy for link development. But moreso, I think that the time you will spend doing this form of strategy would be better spent on social media where you can reach out to customers on real time.