Your iPhone won't backup probably because of photos, I'm guessing.
You have a phone that's 16, 32 or more GB, and a lot of that is filled with photos and videos, but Apple only gives you 5 GB of free backup space. No wonder you can't back up.
To see what's filling up your iCloud storage:
Settings - General - Storage & iCloud Usage - Manage storage (of iCloud, below, not internal phone "Storage" above). You might see other backups there, apps, etc.
My cheap solution? Google Photos. Download the app. Backup all your photos (free!!) to Google. It might take literally a day or two (or more, depending how much access you have to wifi) to back up everything.
Once you've verified every photo/video is backed up to Google, you have accomplished 2 things:
1. Your photos and videos are finally all backed up, which they weren't before because you ran out of space.
2. Now you can turn off the option to back up photos to iCloud, and then the rest of the items on your phone can backup properly. Turn it off in Settings - iCloud, and then turn the Photos toggle to Off.
Or you could just lay out the cash to upgrade your storage on iCloud.
