Why A perfect op-amp would put out exactly zero volts when both inputs are at the same potential, but real devices have small mismatches in the input transistor pair. Input offset voltage is the small differential voltage you must apply between the inverting and non-inverting inputs to force the open-loop output back to zero. It is typically a few microvolts to a few millivolts, and it matters most in high-gain DC amplifiers where the offset gets multiplied by the closed-loop gain.
Watch out The choice about the potential between the input terminals in open loop describes the normal input difference, which for a stable circuit is essentially zero; offset voltage is specifically the correction voltage needed to null the output, not whatever happens to be present.
Offset = the tiny nudge at the inputs needed to null the output. Think "zeroing the scale" before weighing.