volt sec
Faraday's law states that:
ΔB=U*t/(Ae*N),
where ΔB is the flux swing, U the applied voltage, t the time the voltage is applied across the inductor, Ae the effective area of the magnetic core and N the number of turns in the inductor.
As you can see the numerator is voltage*time, that is V*µs.
Thus, the volt-microsecond rating gives you the saturation limit of a particular inductor.
The manufacturer knows the magnetic core, its maximum allowable flux swing before it saturates, its effective area, the inductor's number of turns.
From all these values you could calculate ΔB yourself, but you would have to do it for each inductor and you would need to know all those parameters.
So, instead of all the above details, the manufacturer gives you an easy way of selecting inductors: you get the inductance, DC resistance and V.µs rating. You can tell at a glance if the inductor suits your application or not: you know your maximum voltage and maximum on time (from frequency and max duty-cycle). Multiply them and then select and inductor whose Vµs rating is higher than that.
It makes your life easier.