The resistance of a conductor is said to be 1 Ω if:
1 ampere of current flows through it when the potential difference across the ends is 1 volt
According to Ohm’s law V=I×R where V = voltage, I = current and R = resistance.
Therefore, R=VI=1V1A=1 Ω
Thus 1 Ω is the resistance any material offers to flow of 1 ampere of current when the difference of potential applied between the two ends of the material is 1 volt.