OneDrive is a part of your Office 365 account that provides file hosting services, allowing you to upload files and easily access them from a web browser, or from mobile devices. OneDrive storage is similar to your campus H: drive storage in that OneDrive is intended for personal versus department use. However, as a member of UW-Eau Claire, OneDrive also allows you to share files with other UW-Eau Claire account holders and work on documents simultaneously, making OneDrive a handy tool for collaborating with colleagues.
One difference between OneDrive and your H: drive storage is that OneDrive is stored in "the Cloud" rather than on campus servers. Microsoft controls back-up, recovery, and security. Files are encrypted both in transit and at rest, so security should not be a problem. However, while OneDrive's share feature works well for collaborating with colleagues, the fact that you can easily share files and folders on OneDrive means you also need to be vigilant as to what you are sharing (and with whom).
As with your current H: drive, certain types of information should not be stored on your OneDrive. This includes personally identifiable information such as social security numbers and bank account numbers, information of a confidential or sensitive nature, and anything that could be considered a source of record, such as the sole copy of a certain file.