Criticality-One is NASA-speak for a Space Shuttle point of failure that is single point catastrophic. In other words, a failure for which there is (and perhaps can be) no backup or emergency plan. For example, a Solid Rocket Booster explosive bolt failing to fire leaves one of the SRBs attached (likely badly) to the External Tank. This will unbalance the Shuttle at the least, and the small thrusters on the nose of the SRB may fire their plumes into the External Tank, damaging it and/or detonating the hydrogen and oxygen stores inside.

In other words, Criticality-One is bad.

One step below this is Crit-One-R.