The volt-second time constant gives an indication of the lowest frequency that can be passed without saturating the core of the transformer. The primary winding has inductance that magnetizes the core and if the product of voltage and time is too great the magnetic flux in the core reaches a level of saturation where problems occur. Those problems can be distortion of the output signal or overheating.
Power transformers tend to have a big volt-second constant to be able to deal with low power frequencies (50 or 60 Hz) at high input voltages (typically 100 to 300 VRMS). This makes them physically larger than an equivalently powerful transformer used in a switch mode power supply operating at (say) 100 kHz. This is because the primary inductance of a regular power transformer has to be in the order of 1 henry or above. That needs a lot of turns and makes the device physically larger.
For a pulse transformer, the main criteria is isolation and the ability to transmit a decent shaped signal (typically a square wave of limited amplitude, maybe 10 or 20 Vp-p) of a frequency that is usually greater than 10 kHz. This means that its primary inductance can be very much smaller than a power transformer and hence, its physical size is small.