They are a copy of your data that resides on your laptop/PC and will periodically sync with the server.
Offline files make it possible for you to take your laptops home and still access your My Documents and Desktop. When you return to school any changed data will sync with the server so that your data is backed up or accessible from another laptop/PC.
Sometimes however, the offline files can run into problems and needs to have some manual intervention for the Sync Client to know what to do with the data. You may notice a change in the offline files sync client icon on your task bar, usually it will look like the image to the right.