A proportional counter is a measurement device to count particles of ionizing radiation and measure their energy.
A proportional counter is built the same way as a Geiger counter, but uses a lower high voltage: Any incoming ionizing particle ionizes the gas inside and so allows for a current to flow between the two electrodes (a metal wire in the middle of a metal can is positive electrode and the metal can itself is grounded, i.e. it is the zero voltage electrode). Now, for a Geiger counter the voltage is so high that the electrons that separated from the gas atoms are accelerated so strongly that they knock off other electrons from their atoms which in turn do the same and so on, producing an avalanche, so that every particle, even with a low energy, gives rise to a high current which is easily detectable, but largely independent of the particle's energy.
However, if the voltage is lower, no avalanche is formed. Instead, only those electrons and ions produced by the particle itself are drawn to the electrodes. By measuring the total charge (time integral of the electric current) between the electrodes, we can find out the particles kinetic energy — because the number of electron/ion pairs produced by a traversing particle is dependent of its energy, and —if the voltage is chosen right— actually proportional to it.
Hence, if you lower the voltage of a Geiger counter to the proportionality range and fit it with a sensitive amplifier and a charge integrator, you get a proportional counter. On the other hand, most proportional counters can be switched into "Geiger mode", i.e. the voltage is increased to get an avalanche and make the device work as a Geiger counter.