Firefox bookmarks "live" on one computer, but can be backed up any time and moved to other computers as needed. This process is recommended in preparation for summer computer maintenance, during which all information will be erased.
1) In Firefox, choose "Show All Bookmarks" from the Bookmarks menu (in older versions this might be "Organize Bookmarks")
2) Click the star icon at the top of the Bookmarks window (Mac) or the "Import and Backup" drop-down (Windows) and choose "Backup." Save the file to a network location for future use.
To restore your bookmarks to another computer, follow the same process but choose "Restore" instead of "Backup," then browse to the saved file.