I've heard different things. What exactly is inability to pee?

Urinary retention. Can be caused by blockage as in an enlarged prostate or stool impaction (severe constipation) or bladder stone causing obstruction, neurogenic bladder dysfunction where there is temporary or permanent nerve damage and the urinary sphincter can not relax and allow bladder to empty, or infection causing swelling of bladder neck and hence blockage. Needs care by a urologist.
Urinary retention. If you can let the urine out...Can't pee....And you try and try....You have urinary retention....Pain ensues and you will need to go to the er...If you just don't have to go for along periods of time, more than a day you may have kidney problems....See your doctor.