This means that when you double-click on certain types of files, they will automatically be opened within ONE.
For example, .xls files are ordinarily associated with Microsoft Excel. Thus, whenever you double click on a .xls file, the file is opened by Microsoft Excel. However, if you install "ONE" without unchecking the box next to "Numerics", then when you double click on a .xls file, this file will be opened by "Numerics".
If you want to restore your file associations, run the "ONE" uninstallation program.
You will be given several options: select "Restore document file associations". Doing this will reset your computer's file associations to what they were prior to the installation of "ONE".