Input offset voltage is the voltage source that would be connected to an input of an ideal op-amp to model the behavior of real op-amp.
You can also think of it as the voltage (assumed that both inputs are within the operating ("common mode") range of the chip) that must be applied differentially to cause the output voltage to go to 0V (bipolar supplies) or perhaps midway between Vdd and GND (single supply). AD defines it thusly in the below-linked paper, but it's not inclusive enough for my liking:
Offset Voltage: The differential voltage which must be applied to the input of an op amp to produce zero output
It's a bit hazy what the output voltage condition is (you can think of this as the "output offset"), and open-loop gain is so high that it usually doesn't matter. For example, a precision amplifier might have an open loop gain of 10^6 so a few volts at the output represents a few uV at the input. AD skirts the issue by assuming bipolar supplies. You can certainly test a single supply 3V op-amp by applying +/-1.5V supplies which matches my definition.
Here is one way in the real world to measure input offset voltage, as described in this paper from Analog Devices:
R1 and R2 are chosen to give high gain (but much lower than the open-loop gain) and there is a mirrored pair on the non-inverting input to null out input offset current. R1 is chosen to be very low value to minimize the effects of input bias current. The gain is chosen so that the output will not saturate even for maximum specified input offset voltage and also such that the open loop gain will not unduly affect the accuracy. A 25uV Vos results in an output voltage of about 25mV in this case.
With, say +/-10V supplies, and an op-amp that can swing within 2V of the supplies, this circuit will work with offset voltages of up to +/-8mV, which covers most op-amps. A +/-200nA input offset current will result in an error of +/-2uV in the Vos reading. Most modern op-amps with such a high bias/offset current are bipolar low noise types that run the input transistors at relatively high current, and do not have particularly low Vos, so it's not much of a concern usually.
Here is another method that is somewhat similar but assumes lower input bias currents (potentially more error) and drives the output to zero (via the integrator formed by the auxilliary amplifier) almost exactly (potentially less error due to finite gain of the Device Under Test) Vos is approximately 1/1000 of the voltage at TP1:
In general, the input offset voltage is measured at the output and we apply a calculation to determine the input-referred offset voltage. It's more general for a specification since the output offset depends on the gain in the particular circuit.
There is an analogous situation in the measurement of noise where we measure the noise at the output of an amplifier but divide by the gain of the particular circuit in order to determine the input-referred noise.
If you had a circuit different from a typical op-amp in that the open-loop gain was relatively low, the output offset might not be as well predicted by multiplying a fixed input-referred offset by some variable gain number and you would need two numbers to be specified.