Early smoothbore muskets received lead balls through the muzzle. The balls were smaller than the diameter of the bore, so that, upon firing, they bounced along the barrel until they exited. That bouncing didn't do much for accuracy. Then, in the 15th century, German gunmakers invented rifling – the process of cutting spiral grooves into the inside wall of the barrel. These grooves dug into the projectile as it moved down the barrel, causing it to spin and giving it a truer flight. Rifling worked better if the projectile fit snugly in the barrel, which meant lead balls needed a cover, or patch, to increase their diameter.
A major breakthrough arrived in the 1850s, courtesy of a French army officer named Claude-Étienne Minié. His eponymous bullet was still made of lead, but it was conical, not round. When hot gases from black powder combustion expanded into the hollow-based Minié ball, they caused the soft bullet to flare out and grip the rifled barrel. This meant that the innovative bullets could be made smaller than the bore without diminishing the spin they acquired. And they didn't require a patch, which made them easier to load.
The Minié ball -- the first cylindroconoidal bullet -- improved the accuracy of shooters tremendously. During the Civil War, which saw the first widespread use of these bullets, Union and Confederate infantrymen hit their targets more often and at far greater distances.