You can download from the Files and Photos sections.
You can navigate your folder structure as you know it from your computer. Select a file to open and view it. If the file type is not supported for in-app viewing, you will be asked if you want to open the file in another app.
Tap a photo so that the photo is displayed on full screen on your mobile or tablet. Then select the Open in icon and confirm the action you want to take with the photo.
Note: You can not download an entire folder or many photos at once to a mobile or tablet.