We use OneDrive for storing backups and uploading stuff like photos, videos, music files seamlessly from our Windows Phone devices. But while we can sync OneDrive to our Windows devices like PC / Tablets for offline access, we can’t do that on our Windows Phone devices.
That may change soon though. In reply to an uservoice suggestion regarding OneDrive offline access for Windows Phone, Microsoft has replied in affirmative and has confirmed that they intend to bring this feature, though there is no said timeline.
Windows 10 has brought new OneDrive feature of selective sync with it for Desktop / Laptop, so may be Windows Mobile 10 will be the one that will bring OneDrive offline access feature to Windows Phone.