Guns are the key to victory. Without them, you can expect to be trounced - either by the natives, enemy colonies, or Europe herself. Guns are used to arm your citizens as well as to construct warships.
To construct Guns, you must first have Tools available and have an Armory, Magazine, or Arsenal building. If you have Tools, you can assign a unit to the Gunsmith profession; that unit will immediately begin turning tools into Guns.
Once you have Guns available, you will be able to assign units to the Soldier and Dragoon professions (you can only assign a unit to the Dragoon profession if you also have sufficient Horses available). As well, if you have sufficient Guns available when your settlement is attacked, your citizens will automatically arm themselves and attempt to fight off the onslaught. Guns are also necessary for the completion of the game's two warships: the Frigate and the Ship of the Line.
Gunpowder was invented in the 9th century in China, where it was primarily used in fireworks displays. Once acquired by the Arabs, however, the noisy powder was put to a new use - launching heavy balls of stone or metal through the air at incredible speeds. By the time black powder was being deployed on the battlefields of Europe in the 15th century, gunpowder weapons had become portable enough to be carried by a single soldier. When the Europeans arrived in the New World, firearms were a decisive factor in the European dominance over the natives.