The iOS app GoodReader is great for working with all sorts of files on the iPad and iPhone.
You can create a startup password, but you can also create an extra password to protect extra-sensitive files and folders. This video shows how to set that up.
View the video below, or click here to watch it on YouTube. If you are able to, I recommend that you watch it with HD turned on.
This video on password protecting files and folders in GoodReader is part of a series of quick videos on paperless tips and topics. View more in the series here.