In case you have more than one Dropbox account, it's becomes not easy to manage them on an Android device with the official Dropbox application. It supports only one account at a time so you have to log out each time you need the files stored inside another storage. But there is a way to manage multiple accounts at the same time without the need to log out.
What you need is:
- A file manager for Android (for example I'll use B1 File Manager, which you can download from Google Play for free: https://play.google.com/store/apps/details?id=org....). You can learn even more details here: http://blog.b1.org/how-to-manage-multiple-dropbox-...
- Several ready Dropbox accounts, of course.