What happens if I do not back up my iPhone to iCloud?

Nothing happens. Your iPhone will continue to function normally.

There are benefits to backing up your iPhone and the biggest benefit is having the ability to restore your data if you happen to accidentally delete it or if you want to restore the data to a new device.

Axel F.

Nothing -- except if your phone is lost, stolen, or broken and you don't have a backup, any data that isn't synced with iCloud will be lost and not recoverable.