If you are not sure if your iCloud Notes are syncing check the status on two devices. Eg if you created a note on your Mac, you can check if it was synced to iCloud by opening your note on your iPhone or iPad.
If you don't have two devices from Apple you can always check the sync status using your browser. Just open iCloud.
If you see that Note is in the same state between two devices - it means syncing is working.
Another common issue is that sometimes people create notes not in iCloud but locally. Local notes are not synced across devices.
iCloud Notes are available under iCloud section. Only those notes are expected to be synced across devices.
If you did everything correctly and your notes are still not synced - try restarting Apple Notes application. This usually helps.
When the syncing is happening you should see small spinner.
iCloud Notes supports version history. You can see what changes were made to each iCloud note. You can see content of the change, author and date.
Version history looks like this.
iCloud Notes history is enabled by default, but to see it you need to activate "Show Note Activity" view.