If you upgrade your notes now with iOS 9
While you can upgrade your notes now on your iPhone, iPad, or iPod touch with iOS 9, you won’t see the new features on your Mac until you download El Capitan. The notes on your Mac will stay the same and they won't sync with your iPhone, iPad, or iPod touch that have upgraded notes.
If you want to create and edit notes on your Mac and see them later on your devices with iOS 9, go to iCloud.com.
If you wait to upgrade your notes with El Capitan
When you download El Capitan and open Notes for the first time, select Upgrade Now. The notes on your Mac and iOS devices will automatically upgrade. And if you sign in to iCloud with the same Apple ID on your other devices with iOS 9 and El Capitan, any changes you make to a note on one device instantly appear on all your other devices.
Make sure your notes finish upgrading before you leave the Notes app.
Learn more
If you’re signed in to more than one iCloud Mail account on your iOS device or Mac and have notes syncing turned on, you can only use the new Notes features with your primary iCloud account. You can see your primary account in Settings > iCloud, or System Preferences > iCloud.