I can't activate my iPhone

What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support

Tell (or ask) them to flow the steps in the link above.

I suspect it's broken and you should get your money back.

But this may help in the meantime: https://support.apple.com/en-us/HT201407

~Lyssa

What message, exactly, is on the phone's screen?

~Lyssa

Give the device back to the person you bought it and ask them to properly prepare it for reuse.

It is locked to Find My Phone and without their help you can't use it.

The Activation Lock that QuickTimeKirk is referring to is a different message - and might still be part of your problem.

Follow my link for troubleshooting.

~Lyssa