Various power-converter architectures use their transformer in different modes. In continuous conduction mode (CCM), the magnetic field never completely collapses due to the transformer's mode of operation. Instead, the energizing portion of the electromagnetic cycle begins before the de-energizing portion of the cycle completely converts the stored magnetic field back into electrical current. If you imagine the triangular current waveform that results from a square-wave voltage drive on the primary, the current in a transformer operating at steady state in CCM never reaches zero. Instead, it begins to ramp back up from a positive, non-zero, local minimum.
Under discontinuous conduction mode (DCM), the field collapses fully and some interval follows before the onset of the cycle's energizing portion. This mode makes better use of the electromagnetic structure and the primary circuit's energy than does CCM, because it doesn't maintain a constant field from which the secondary extracts no energy.
Between the two is the critical conduction mode (CrCM), in which the energizing portion of the cycle begins as soon as the field fully collapses. Though CrCM generally requires simple primary-side control circuitry, it produces high input-current ripple (a consideration in some applications), higher EMI, and greater electrical stress on the primary-side switches. It is also, by definition, a variable-frequency control mode. Thus, it's not practical in applications that require converter synchronization.
By comparison, CCM requires a more complex primary-control circuit, but generates small input-current ripple, allows fixed-frequency operation, and is compatible with synchronization methods.