I’m a self-employed contractor. Sometimes I will get a check from a client and take it to their bank to cash it, instead of depositing it in my own bank.
For anyone who doesn’t know the drill: You’re always required to hand over your drivers license or other ID, sometimes along with a second piece of ID (eg credit card.) Once the check is deemed good, they want your fingerprint on the front of the check. Some banks also make a copy of your ID, and some ask for a phone number, which is written on the back of the check under your signature.
So, the teller types my drivers license number (presumably) into the system. This is followed by a flurry of other clicking and typing, while the teller watches whatever comes up on the screen. The s/he says thanks hands the ID back, finishes the transaction and hands over the cash.
My question is: What information relevant to my ID comes up on the teller’s screen?
Nobody knows this?
I know it’s not earth-shattering, but surely someone here is or has been a bank teller? Or maybe it’s really that super-secret… 
My anecdotal experience: your ID? If you aren’t a customer at the bank, then we have none of your information. Do you think banks access some national database? Nope.
All I’d do is type in the information, e.g. DL number and expiration, state. Then information for the second ID, which for credit card was only, IIRC that it was a CC and the expiration date. The number is not recorded, but we were supposed to verify the name, of course.
We would also see the account that the check is drawn from, such as name, address, phone, and most importantly: funds left in account, and and special holds or questionable things on the account.
My bank teller experience is decades out of date, but my guess is that they are simply documenting the fact that they checked your ID.