Microsoft is said to be working on providing offline access to OneDrive files on Windows Phone.
OneDrive on Windows has the ability to store all of your files locally and sync the changes as and when they happen in the specified folder. However, such functionality does not exist on the OneDrive mobile apps - but it could become available in the future, judging by a Microsoft exec's statement.
On the OneDrive User Voice forum, a Windows Phone user suggested that Microsoft should bring offline access to files on the platform similar to that on the desktop version. The suggestion was marked as "in the plans" by Casey Penk, a Program Manager at Microsoft, but there may be some time yet before the feature actually reaches the users, as Penk has mentioned that there is no fixed timeline for its delivery.
It was reported recently that OneDrive would be getting a music storage feature and the ability to stream using Xbox Music. The addition of this and other new features such as offline access will no doubt be welcomed by Windows Phone users.
Source: User Voice