What is using so much storage in my iPhone?

You should be backing up the phone frequently; ideally, you should enable automatic overnight backup. But for this problem your phone probably has storage corruption, which can be caused by an interrupted sync. You can try fixing it yourself:

• Back up your phone to your computer, iCloud or both (for belt-and-suspenders added security)—>How to back up your iPhone, iPad, and iPod touch - Apple Support
• Restore the backup you have just made—>Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Here is additional information on Other—>What is "Other" and what can I do about it?

Most likely they are corrupt files. Which iPhone do you have, which version of iOS are you running and have you tried restoring your iPhone from your backup?

That doesn’t matter. The explanation of Other is the same in iOS.

Yes, or you can back up to your computer or both for extra comfort. Note that if a computer backup is not encrypted health data and passwords will not be backed up, but don’t forget the backup password as there is no way to recover it. An iCloud backup is protected by your Apple ID password and does not have a separate backup password.