What does the term unlocked with verizon mean?

I was pre-ordering iPhone Xr, and chose Verizon as my carrier. At the last step, beneath the price, "unlocked with Verizon" was written. Could this device be used with international carriers?

As long as it's unlocked, yes, but you would have to find an international carrier that can support that particular iPhone.

It means that the phone is not tied to Verizon. This means, that in theory, it will work with any compatible GSM carrier around the world. It ISN'T guaranteed to work on every carrier around the world, though. Of course, if you buy the phone with a 2 year financing agreement, you're still responsible for paying off the phone. If you don't pay it off, Verizon will blacklist the phone and it will be pretty much useless with any carrier.

Verizon sell their phones unlocked, so yes it can be used with other carriers.