On the RTP-SC desktops, as on all Linux systems, the home directory is where you end up after you log in. This is where you will probably work from, and where you keep documents. This area is fully backed up to a store in a different building once a week, in case of disaster, and regular snapshots are kept, in case you delete or lose important files. There is also a storage area, which is snapshotted but not backed up. More details are available here using your RTP-SC login details.
Note: the phrase 'back-up' is often used to mean any kind of data duplication, for example keeping two copies of an important file. In the link above, backups refer to a copy on a separate storage system, so that data can be recovered in the event of catastrophic failure. Snapshots are copies of files on the same disk which allow for recovery of accidentally deleted files, and some recovery of corrupted or edited files.
In general, any code or documents should be kept in your home directory. Large data files which can be reproduced, albeit with effort, can be kept in storage. If something cannot be reproduced (for example, real-time data) you must ensure it is backed up in some way. Snaphots of home and storage are run about once per day, so for important files such as papers consider the RTPSC cloud storage, or make regular copies yourself.
Scratch data (for example, large writes while a program runs which aren't needed afterwards) should never be written to your home directory. There is a dedicated space for this, /tmp. Tmp directories are usually temporary, as the name implies, and files are deleted after some period of time.