Here is the help topics about security. Lots of answers. A chat box popped up and Travis the rep said this:
Security is our top priority. To start, we use SSL for data transfer, creating a secure tunnel between Dropbox applications and our infrastructure. Then, we encrypt your data with 256-bit AES encryption in transit and at rest. We also break down all the files into 4MB blocks and store the blocks in a separate server than the metadata of those files.
(My note: the files are unencrypted on your hard drive, but encrypted in storage online.)
This is their “Is Dropbox safe to use?” answer.
Something I forgot to note earlier, they store 30 days of previous versions so if you accidentally save over a file, you should be able to recover the original version for a month.
This is a PC Mag article on how to make it more secure. It links to an article about a data breach in 2012 and Dropbox’s statement on what they’re doing to beef it up in 2014. The PC World article points out that one issue for many people is the use of weak passwords, so make sure your passwords are up to snuff.