It's usually circular, and usually has a circular hole through the middle down which the bullet, shot or shell travels after the propellant is ignited and gas pressure forces the projectile towards the muzzle. The hole through the middle is called the bore. The diameter of this hole is called the calibre.
Generally, the longer the barrel, the higher the muzzle velocity as the propellant gas has longer to act. The accuracy is also usually improved by a longer barrel as the projectile has longer to be pointed in the right direction before it leaves the muzzle.
More on this wiki page.