Gas furnace is leaking water when air comnditioner is running any ideas what problem is and what can I do to solve it , is problem serious

It's supposed to leak water, but in a controlled way, AC removed humidity from the air.

You didn't say where it's leaking and that can provide a clue. Post a pic of the condensate piping and where the leak is and you might get better help.

Mold and mildew problems will occur if it's not fixed. Meaning, your indoor air quality will suffer.

The (Evaporator Coil) sits on top of the furnace and cools air that flows through it...

This coil sits in a moat type pan with a drain that runs to floor drain

Usually the coil needs to be cleaned and drain line unplugged

http://www.rd.com/images/tfhimport/2001/May01_Air_Conditioner_Clean/20010501_Air_Conditioner_Clean_page002img001_size2 .jpg

Click to enlarge for better view of picture