Go to Settings » Backup and import » Create backup of all notes. A backup file will be created and stored on your phone’s storage. You should immediately send the backup file to a safe location (like Dropbox or Gmail) by pressing the Share… button or by manually copying the file to your computer using a file manager, so you can restore your notes when you lose your device.
Note: you can directly open the file from other apps like an email client or file manager. It will start Notes and ask if you want to import the backup. See Importing a backup for more information.
Note: the backup files are not encrypted.