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 also allows you to share files with other users and work on documents simultaneously, making OneDrive a handy tool for collaborating with colleagues.
Note: OneDrive information 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).
Also note that 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.