"Why do they call the digital fund transfer app on my pocket computer a 'checkbook'?"
As many banking activities such as cashing checks, deposits, transferring funds, and paying bills are handled through mobile apps for smart phones and computers, we can only imagine that activities like balancing a checkbook on pen and paper will become extinct in the next few years. It's hard to gauge what term will replace "checkbook" in the future, but many adults today won't miss the free plastic checkbook covers that accompany paper check refills.