Back when I used checks a lot (before heavy ATM card use), I balanced my checkbook. So, say you had $548.78 in your checking account. You'd write a check for $10.78. You'd write in the ledger that your wrote a check for $10.78, and the new balance was $538.00. You did this every time you wrote a check, if you were on top of it. If not, you had to go back, apparently surrounded by papers, trying to balance it so you know how much you had in the account.
Nowadays, I still write a few checks, as some places don't have online portals, or they charge an $8 fee to process the online payment. But, I never, ever balance my checkbook any more. I simply go online and look at my account every few days. In fact, I would never know if a check made it somewhere unless the company contacted me. I think very few people actually balance their checkbooks these days.
Was the show you were watching taking place years ago?