I have an iPhone 5c that is not eligible for iOS 11. I don't want to have to buy a new phone if this one will still work, so is there a way to jailbreak the phone and install iOS 11? Or does it not work like that? Thanks for any help, I'd like to understand how this works.
No, this is not possible.
I don't want to have to buy a new phone if this one will still work...
Your iPhone will still work with its current operating system, though. Don't feel you need to upgrade, only get a new phone if you really want to.
As to "why", there are many reasons. For one, as Mike Scott mentioned, the iPhone 5c has a 32-bit processor, and iOS 11 requires a 64-bit processor to run. Secondly, the operating system has various aspects which rely on the exact device you own. Depending on whether you have an iPhone or iPad, a GSM or CDMA phone, and so on, you need to have a slightly different version of the operating system. In order to run on a certain device, Apple needs to develop a version of it specifically for that device.