Cavitation occurs when the pressure on a liquid drops below the vapor pressure for the liquid or when gas is otherwise introduced to a pump such that it disrupts the flow of the liquid through the pump.
Positive displacement pumps trap a quantity of liquid (or gas) and then increase the pressure by pushing (displacing) it into the discharge pipe. External pressure pushes the liquid into the pump chamber which then is made smaller before the pump chamber discharges its contents. If any gas enters the pump chamber along with a liquid it is simply compressed along with the liquid. Positive displacement pumps work just fine with both gases and liquids - although when gases are being compressed it is usually necessary to cool the pump chamber which heats up quite a bit during the almost adiabatic compression step of the pump. Cavitation does not occur in part because the pressure in the pump chamber is almost completely uniform. If the compression chamber drops below the vapor pressure of a liquid being pushed into it, the external pressure will continue to push the liquid in, then when the pump begins to decrease the volume, the valve allowing the liquid to enter will close and the volume of the contents is decreased until the pressure rises back above the vapor pressure of the liquid and it condenses in the pump chamber.
A centrifugal pump uses a rotating impeller to increase the pressure and flow rate of a fluid. In centrifugal pumps, pressure is added by increasing the kinetic energy of the liquid and then, in essence, "throwing" the liquid into the discharge pipe where the higher kinetic energy liquid pushes on the liquid ahead of it to increase pressure. As the impeller moves through the liquid being pumped, it pushes on the liquid ahead of it, imparting additional kinetic energy to it. The liquid behind the impeller, however, actually experiences a little bit of a drop in pressure as the impeller tries to move away from it. Because liquids are fairly incompressible, this usually does not create any problem and the internal pressure of the liquid is sufficient to keep it in contact with the backside of the impeller. If the drop in pressure is low enough that the pressure drops below the vapor pressure of the liquid at the temperature present in the pump, the liquid will begin to vaporize. Once gas is present in the pump, it begins to cavitate - the liquid separates from the back of the impeller - especially near the tips. For this reason, introducing air or other gas into the liquid can cause cavitation, even if the pressure never drops below the vapor pressure of the liquid being pumped. This is also why centrifugal pumps are usually "primed" prior to being started up - to get all, or at least most, of the gas out of the line so that the pump won't cavitate.