“Bank of America Corp. has lowered its prime-lending rate to 7.75 percent from 8.25 percent, effective Tuesday.
I am as ignorant on these topics as the next guy, but isn’t prime rate the rate at which the bank lends short-term money to credit cards and such rather than mortgage?”

Yes,

The prime rate, as reported by the Wall Street Journal’s bank survey, is among the most widely used benchmark in setting home equity lines of credit and credit card rates. It is in turn based on the fed funds rate, which is set by the Federal Reserve.