When one measures the resistance of a superconductor by placing it in some electrical circuit, in series with a voltage source V (eg. battery), and measure the resulting current. If the resistance of the remaining circuit elements (such as the leads connecting the sample to the rest of the circuit, and the source's internal resistance) is R, the current passing through the sample is V/R. According to Ohm's law, this means that the resistance of the superconducting sample is zero.
Source:http://en.wikipedia.org/wiki/Superconductivity