Dropbox can be used to transfer PDF and text documents to an iOS device (iPad, iPod, iPhone), Android, Windows or Mac. Some Apps allow you to download documents directly to the App using the tablet's browser, and some Apps let you share and sync your files from inside the App.
Each device and App handles Dropbox connectivity differently, so you'll need to take some time to explore the different characteristics.
Here is a short list of Apps that either include Dropbox or an internal Browser:
DeepDish GigBook (iPad)
MusicNotes (iPad, Android)
MusicReader (iPad, PC, Mac)
Noteflight (PC, Mac)
General instructions for using Dropbox:
Copy the files to Dropbox
View (which may take you to a website)
On the tablet, tap the file you wish to download
Tap the Open With icon (several small boxes lined up vertically)
Choose the App you want to download the files to