If you've ever connected your iPhone to a computer before, iOS would prompt you to "Trust" the computer and enter your passcode to confirm. According to Apple, trusted computers can "sync with your iOS device, create backups, and access your device's photos, videos, contacts, and other content." This is a lot to give a computer access to, especially if you do so with one you don't want to always trust.
There are a number of reasons why you'd want to untrust a computer. Maybe you had a friend load up your iPhone with some cool ringtones they created in iTunes. Perhaps you trusted a computer by mistake because you just wanted a quick charge. Or, maybe it was a public computer that you used Image Capture on. Either way, it's good to do in case someone ever gets a hold of your iPhone and has access to the same computer.
Also, there's "trustjacking," a new type of attack hackers are taking advantage of. Once you've authorized a computer access to your iPhone — even if the "computer" just looks like a normal charging station you'd find out in public areas — your iPhone can then be attacked while connected to the same Wi-Fi network as the computer, leading hackers to install malware, spy on your usage, take backups of your photos and call logs, and just about anything else you can think of.
Untrusting a computer isn't hard, even though you aren't able to pick and choose which computers to untrust — you have to disengage from all of them all at once.
There are three options for untrusting computers, listed here in order of least annoying to most annoying. For example, Option 1 won't be too disruptive for you, but Option 2 will require more work to get your iPhone back to its previous state. Each of these has positive aspects, side effects that you may find beneficial, so be sure to read through to the end to see which of these is right for you.
This is by far the least intrusive way to untrust a computer. By performing this method, all you'll need to do is re-enter the credentials for Wi-Fi networks you commonly connect to. You can even think of this as a plus of sorts, as your iPhone will no longer connect to the myriad of unsecured public networks you potentially accrued along the way.
So, first open up your Settings, then go to "General." From there, tap "Reset," then "Reset Network Settings."
You'll need to enter your passcode before you're able to reset your settings. After you do, tap "Reset Network Settings" on the confirmation prompt, and your device should restart. You should immediately go to your Wi-Fi settings after this, as you'll be logged out of any network you're currently connected to.
Resetting "Location & Privacy" settings is a more intrusive way to untrust a computer. What this option does is reset all the permissions you've granted other apps. This includes location, camera, photo, contacts ... everything. If you have some apps that you regret giving certain permissions to, this could be a good catch-all to bring everything back to center.
The process to do this is nearly identical to the one above. Instead of tapping "Reset Network Settings," though, hit "Reset Location & Privacy." You'll need to enter your passcode again and select "Reset Settings" after you do so to complete the process. Your device may restart.
Now, every time you open an app, though, you'll need to re-grant it permissions that you previously gave it before (or choose not to grant it if that's the case). It can be kind of annoying, so go with Option 1 if you're unsure if you want the hassle of all this.
Restoring your iPhone to factory settings is the most damaging of these options. It'll completely wipe your iPhone of your contacts, photos, files, apps, and everything else. Before you choose the option from the "Reset" menu — titled "Erase All Contents and Settings" — your iPhone will prompt you to back up everything on iCloud so you're able to restore it later.
While this option will do the trick, I wouldn't suggest it unless you were planning on resetting your iPhone to factory settings regardless. It's just too much work to get your iPhone back up to snuff, minus trusted computers.