Cloud storage and file syncing apps seem like a dime a dozen these days. That is not necessarily a bad thing, since choice is one of the best things about technology in general. Each of us here at AP have our own preferences for which services we use — most of us use multiple offerings, actually. One of the biggest names you will hear about is Box, and its Android app got updated to allow for uploading entire folders from your device.
Simply, you select the folder you want to upload from the "Add From Library" option in the app. And that's pretty much it. Personally, I have not had the need to do such a thing from my phone (since I handle large folders on my computers), but I can certainly see the use case here.
If you have never tried out Box before, you get 10GB of free storage for joining. Additionally, you will have access to features like file-specific security options, the ability to view over 200 file types, and document comments for feedback. Having another service to use as a backup for your important files is not the worst idea.