If you're armed, you are carrying some kind of weapon. Armed soldiers are most commonly supplied with guns.
In the United States, police officers are almost always armed, while British police usually don't carry guns. When a crime involves the use of a weapon, it might be described as an armed robbery, and even an animal is sometimes said to be armed: "The cat was armed with sharp teeth and claws against the puppy's enthusiasm." The Latin root is arma, "weapons," or "tools of war."