This article from GlobeLife Work in Canada discusses the findings of 360 Degree Feedback across the US, specifically that managers don't listen to their people enough.
The Boss Isn't Listening
There are some tips for both staff and their managers on giving and receiving feedback in the article. In summary, "if your company does 360 degree reviews, pay attention to them". As a member of staff you have an opportunity to make a difference to how you interact with your manager. As a manager, you can learn a lot from how other people see you.
And for the organisation, ongoing monitoring of 360 Feedback results is a great way to measure what the key management issues are, and how they're being dealt with on an ongoing basis.