iPhone 5c won't update?

Hi

If you are trying to update your iPhone wirelessly, follow the steps here, including for removing any downloaded update, if required, before trying again to update your iPhone to the latest compatible version of iOS:

• Get help with over-the-air iOS updates - Apple Support
• Update the iOS software on your iPhone, iPad, or iPod touch - Apple Support

Also delete any beta profile that may be installed for your iPhone and then restart it after doing so.

If you are unable to update wirelessly, consider instead updating via iTunes (and vice versa):

Update the iOS software on your iPhone, iPad, or iPod touch - Apple Support

Whichever method you choose, be sure to first make a backup of your iPhone (you may wish to choose the option to Encrypt iPhone backup if using iTunes):

How to back up your iPhone, iPad, and iPod touch - Apple Support

Note that, for iTunes to be able to connect with a device running iOS 10 or newer (including updating it), your computer must be running iTunes version 12.5.1 or newer:

Get the latest version of iTunes - Apple Support

You can not upgrade to iOS 10.2. You can only upgrade to the most recent, compatible version, in this case 10.3.1

Jailbroken?

Connecting to a computer that was used to jailbreak?

What version of iTunes is on your syncing computer?

What operating system is on the computer?