Ionization chamber is a device to measure radioactivity level. When air’s atoms are hit by radioactive particles, an ion-pair is produced. Ions has electric charge, if they are in electric field create by positive and negative electrodes, negative ions will move to positive electrode and positive will move to negative electrode. They will try to “meet each other” thus creating a current. This current can be measured. The current is proportional to amount of ion-pairs. Amount of ion-pairs is proportional to radioactivity level.
More details on Gawron’s blog.