It might be that one 'phase leg', as I like to call the individual (usually) ungrounded conductors, has become disconnected after the transformers, or that an entire phase winding (between two {or more} legs) is no longer producing a voltage.
The single-phasing condition can occur on the secondary or primary side of the transformer. It makes a difference as to how the motor is connected and if the source transformer is wye/delta (or delta/wye).
With the loss of one phase on the secondary side, the motor can have two phases with 173% current and one phase with 0% current. Then, a delta-connected motor will experience normal current in two windings and 200% current in the winding opposite from the lost phase. A wye-connected motor will experience 173% current in two windings and 0% current in the winding with the lost phase.
With one phase lost on the primary side of a wye-delta source, the current to the motor can be 115% on two phases and 230% on the third phase.
It is common practice for the utility industry to call each primary conductor of a three-phase system with a multi-grounded neutral a phase. A line with 2 primary conductors and one neutral is referred to as 2-phase or "v"-phase. This recognizes that a load or winding can be connected line-neutral in addition to line-line. A line-neutral voltage can be a phase in the same manner that a line-line voltage can be a phase. Any voltage is defined by the relationship between two points (a designated point and its reference).
That being said, if you just have a delta system (no neutral) and lose one conductor, you are left with only two conductors (two points). Since a voltage is defined by the relationship between two points, this leaves you with one voltage and thus one phase (back-feeding, etc being ignored in this context).