Why would someone be granted a permit to carry a weapon?

Most states are "shall issue" states, meaning that if the person is qualified to possess a handgun under federal and state law, that state must issue a carry permit if the citizen applies properly, passes the background check, pays the fees, etc.

A few states are "may issue" and these states have the power to deny a person a handgun carry permit EVEN IF the person meets all the eligibility requirements under the law. A common situation is the the local permit-issuing authorities want to know what reason the citizen has for wanting to carry a gun, and if they don't think the reason is "good enough" they will deny the carry permit, or maybe only issue a limited transportation permit to allow the gun to be carried to and from the shooting range or the hunting fields instead of loaded carrying on your person for protection.

WHY do citizens want to carry guns? For personal protection against criminals is the most common reason. Sometimes the citizen will be extra-vulnerable to attack or extra-likely to get robbed (like the owner of a jewelry shop or liquor store), but other citizens carry guns for protection just because ANY person could be robbed or kidnapped or attacked by a criminal, at almost any time or location.

Some people have "carry permits" when really they don't want to carry loaded handguns on their bodies or within easy reach. They just want to be able to take the gun to and from the shooting range, or the woods, or the gun store. In some states you can't take a pistol out of your home for any reason unless you have a "carry" license, even if it's broke and needs to go to the gunsmith for repair.