"Backing up" simply means copying important files and folders* to another drive such as:
a USB storage device, or
Google Drive - This video shows you how to copy files and folders to your Google Drive.
These are the items you should copy:
Documents Folder - This is where we SHOULD save our documents
Desktop Folder - This is where most of us DO save our documents
Movies - This is where iMovie Projects and movies and TV shows are kept.
Pictures - This is where your pictures in iPhoto are kept.
Music - This where your iTunes music library is kept.
Downloads - This is where all your files from webpages get downloaded.
Web browser's bookmarks. - Click here to learn how.
* Important files and folders that need to be copied should be found inside your Home Folder.
When you're in Finder, click on Go > Home.