Generally speaking, conductivity is the rate at which matter or energy can pass through a given material. A material with a high level of electrical conductivity, for instance, would easily accommodate the movement of an electric charge. Of course, this measurement has diverse practical applications, from using conductivity to move heat or energy to using insulation to keep it in place. Each of these uses depends on the kind of activity desired and the kind of conductivity used as a reference.
Thermal conductivity measures the ability of a material to accommodate the movement of thermal energy (heat), measured in Watts per meter Kelvin (W/ mK). Materials with high levels of thermal conductivity are usually used as heat sinks in practical applications, just as materials with low levels of thermal conductivity (high levels of thermal resistivity) are often used as insulation. Although exceptions exist, metals tend to be good thermal conductors and gases tend to be good insulators.
Electrical conductivity, measured in Siemens per meter (S/m), depends on similar molecular structures to thermal conductivity. Metallic and highly polarized materials that conduct heat well likewise are good conductors of electricity. Given the importance of electricity in the modern world--and specifically the importance of moving electricity from generators to users–electrical conductivity is a particularly relevant measurement, used to design electrical transmission systems like copper electrical wires that move energy over long distances with minimal resistance and loss to friction.
Ionic conductivity is a molecular category that measures the ability of a charged particle (an ion) to move through the crystalline structure of a material. Compounds and elements able to accept the movement of an ion through their structure are called electrolytes and are usually solid or liquid. Although ionic conductivity may seem to have fewer practical applications than other and better-known forms of conductivity, measuring and controlling ionic conduction is actually what makes common household objects like microwaves and batteries work.
Hydraulic conductivity describes the rate at which water can move through the porous elements of a surface. Measured empirically or predicted by grain size calculations, hydraulic conductivity is an important consideration for assessing the permeability of soils, rocks and plant layers. Such studies provide critical information for watershed management, agriculture and flood prevention. Hydraulic conductivity also is used to model the behavior of aquifers and subterranean water deposits, shaped by the ability of water to move horizontally and vertically through different materials and geological layers.