This is a Second Amendment question. Arizona currently permits its residents to carry a firearm without restrictions provided it is out in the open, that is, the gun must be visible to others. A person can carry a concealed weapon provided they get a permit through the Department of Public Safety, which requires the submitting of fingerprints and taking several hours of training. A new bill would remove the requirement of obtaining a concealed weapons permit, and allow any person to carry a concealed weapon.
Proponents believe that the Second Amendment precludes the government from restricting a person from having a firearm. Proponents reason that since the "bad guys" will not follow the law anyway, that law abiding citizens should have the right to protect themselves. Also, people in cold country should be entitled to have a firearm under their coats.
Opponents believe that times have changed, and that allowing anyone to carry a weapon without some training and without some restriction risks greater harm to the general population.