I’ll admit that it’s been decades since I used them, but it used to be that you would record the check numbers and keep that information safe. If you lost the checks or they got stolen, you could go to American Express (or whoever the issuing company was) and get them replaced on the spot.
You cash them and/or exchange them for local currency as you need it, so you’re not carrying around a huge bundle of cash. A lot of banks will issue them free of charge to their customers.
Most places are taking travelers checks anymore….either CC or cash. My France trip was over 5 yrs ago and I was told not to bother with the checks.