It's a very simple service, been using it for the past year now. Basically it creates a folder on your machine that is backed up in real time over the internet. It allows easy syncing since any machine you have the application installed on will sync instantly with the dropbox server. Comes in handy when you want access to files in different places such as work, laptop, home etc. I like it since it is an easy way to share files, you make changes to your files and they are synced even if your other machine it off.
A few other bonuses are that it is web based so even on a without the app you could access your files via a web browser and there is also a share option which will let you create a url for any file you want to share publicly.
As with all these cloud services privacy is definitely a concern, look at how much data is already stored with email services. Even when you delete an email, is it really ever deleted? These services could easily archive your data if they wanted to. Ah well ignorance is bliss and the simplicity/redundancy these services offer make em so irresistible hehe.