This term, failure to progress, is simply that. Dilatation of the cervix and descent of the fetus fail to occur despite efforts to correct it. In the recent past, this diagnosis has taken some criticism due its use (or overuse) to justify high c-section rates.
There was a time in recent history (and to this day in some Third World countries) during which FTP was often a sign of a serious problem which could not be corrected. Babies and mothers could and did die in labor due to these “obstructions” of labor. In those times and places there were few reliable interventions or no one to intervene effectively.
However, in a modern hospital, even with a trained professional midwife or doctor, there is some validity to the criticism that Failure to Progess is often a midwife’s or doctor’s Failure of Patience.