I found it an interesting approach to an incentivised tutorial of sorts it's very easy to install Dropbox on your desktop and just forget that it's there. By offering you free storage space by introducing you to features, such as their mobile app, sharing, etc, they're making you curious and interested in what else they have to offer you.
You could call it growth hacking I guess. I think it's an interesting alternative to idk, a weekly "did you know that?" e-mail (e.g. Evernote) or a tooltips-driven tutorial, or Clippy.