The Flintlock Pistol is a hidden weapon, inaccessible in a normal game without cheating or editing. It uses cartridges as ammunition, just like bows use arrows or crossbows use bolts.
It is a very powerful weapon that uses the hidden Firearms proficiency and can shoot bullets at an incredible velocity, faster than any arrow. However, the Flintlock Pistol is wildly inaccurate and the bullet cannot be seen in order to adjust one's aim, making this weapon very difficult to use at range.
Like other ranged weapons, the Pistol has reduced accuracy when on horseback, but the targeting reticule stays perfectly still while aiming. On the downside, this weapon is very slow to reload. Cleaning the barrel and loading a cartridge takes longer than reloading any crossbow.
Note that this weapon is not the same as the firearms featured in With Fire & Sword, which are actually crossbows under the hood. However, the Flintlock Pistol is a likely source of inspiration for them.