It could depend on the state, but in America a driver's license is basically the de-facto form of ID. So, sometime back in the 50's or something, I believe fingerprints started to be taken as part of getting your license so that your fingerprints could be traced back to you for crime purposes. Similar to how in some states when you purchase a firearm, you are required to give the state a spent shell so that the state has a record of the "ballistic fingerprint" of your firearm.

"When" you purchase a firearm?! Only in America ...

Your smug sense of self superiority is so endearing

...or is it concern mixed with fear?

First I've heard of it, and I am American.