As Bennie stated it is the resistance of the electrode(s) to earth. It is a target number the NEC uses in 250.56, but is not necessarily obtainable. If you read 250.56 you can see this by the wording. Drive the first rod and measure, if greater than 25 ohms, drive another and you are done whether or not it is below 25 ohms. What this translate too is you do not have to measure, just drive two rods and walk away to meet the code.
The purpose of the grounding electrode system is to provide an earth reference for the facility and provide a path for lightning and static electricity. Recommended practices is to provide a resistance of 25 ohms or less for any made earth grounding electrode, but one does not need to seek unrealistically low values of resistances such as the popular 1 ohm value. Such connections are only used for electrical safety and are not suitable for use at high frequencies.
Another way to look at it is lower the resistance to ground, the lower voltage potential would be on the metallic noncurrent carrying parts of the system. 25-ohm brings the voltage down to a relative safe touch potential.