See this link from Dropbox. It tells you where they are stored.
https://www.dropbox.com/help/81?path=mobile
Here is how I do it on my tablet:
1. When you log in to your Dropbox in your tablet/phone, find the file you want to open.
2. Touch it to open it via the associated program. When you open it, a copy of it is saved in your cache on your phone/tablet. In my tablet for example I can find it here: /Android/data/com.dropbox.android/
3. Then click the Cache folder or Files folder inside the above path, then keep clicking their subfolders until you will see a copy of the file you just opened earlier saved. You can even see it later off line. If you want to delete it, go to the phone/tablet settings and clear the cache.
Here is an excerpt from the above link:
Local copies of your files download to your phone or tablet whenever they are opened via the Dropbox app. Once they have been opened, you can open them directly from your phone or tablet, even if you're offline. The files are saved directly to your phone's memory in what's called a
cache. To remove the files from your phone or tablet, all you have to do is clear your cache from
Settings