Pantaz called it right. You measure "squisheyness" with a gauge that presses a rounded surface into the rubber under test. The pin is spring loaded, and as the rubber presses the pin back towards the gauge, an indicator gives a readout. As I recall, this continues until the surface around the pin eventually meshes with the rubber. Then you record the reading.
Since rubber varies widely, there are different scales and corresponding tips that you can use.