Electrical conductivity is the ability of a material to conduct (transmit) an electrical current. The inverse of electrical conductivity is electrical resistivity. Electrical conductivity is generally expressed in either Siemens per meter (S/m) or (more commonly) milliSiemens per meter (mS/m). Electrical Resistivity is generally expressed in Ohm.m.
Current can be conducted through a rock through three different mechanisms. These are electrolytic, electronic and interfacial conduction.
It should be noted here that this description of electrical properties only starts to scratch the surface of these electrical properties, and many books and articles have been written (and are being written) on this topic. A more in depth description of this topic can be found e.g. in this nice overview article by Gary Olhoeft or in Chapter 2 of the PhD thesis of Andreas Kemna
When we measure the electrical conductivity of soils or rocks (details on how we do this is provided in subsequent sections) we measure the total electrical conductivity (which is a combination of the three conductivities listed above). This electrical conductivity depends on the electrical properties of all the constituent materials of these soils and their geometric relationships.
There is a good understanding of the values of electrical properties of different rocks and soils (and of the changes caused in these electrical properties due to changes in moisture, precipitation and so on). This understanding (discussed in some detail in the next section) allows us to interpret an electrical resistivity image in terms of geology, hydrology and processes (and is thus the reason why we use electrical resistivity to investigate the subsurface).