A GM counter detects activity even before we deliberately bring any radioactive source near it. This is due to the background radiation that is all around us. There is practically nothing we can do to block out the background radioactive sources because they are in the air, in the soil, in the buildings, in ourselves and even the GM counter itself. What we can do, is to deduct the (average) background count rate from the measured count rate, in order to obtain the actual count rate due to the radioactive source alone.
For your interest, the pie chart below illustrates the major sources of background radiation we encounter in our lives.