Except for one optional feature (noted below), the Dropbox app does not use your device's location data. However, because your photos may contain information about where they were taken, Dropbox (like other apps) needs special permission to access them.
If you turn on the background uploading option in the Camera Upload settings, the app will ask for permission to access your iPhone's location services. This will enable the app to finish large uploads without the need for you to open the app.
Here's how it works: Normally, photos and videos can upload while the Dropbox app is open and for only a few minutes after it is closed. But with background uploading turned on, the app will automatically resume unfinished uploads when it detects a significant change in your iPhone's location. This feature is designed to make your Camera Uploads work more efficiently and does not collect your location information.
Understanding iOS Location Services
For information such as how to tell when an app is using location services, steps to reset or change your location settings, and to learn more about iOS location services, see Apple's Understanding Location Services support article.
Apple's API reference
For iOS developers or highly technical readers, check out Apple's Developer documentation to learn more about the API library Dropbox uses to access iPhone and iPad photo galleries.