Crowning a rifle barrel, in simplest terms, is shaping the muzzle so the rifling's edge is protected from impact. Most factory barrels have
a round, convex-shaped crown from bore's edge to the barrel's outside diameter. That's easy to make and finish, plus looking rather pleasing.
The accuracy part of the crown means the land and groove part of the barrel must let the bullet's base exit evenly all the way around. When this happens, gas escapes uniformly and evenly around the bullet's base. If gas escapes unevenly (poor crown, even unsquare bullet bases), the point of greatest gas release will push the bullet in the opposite direction and tilt it. Tilted bullets leaving the barrel just don't shoot straight; how far they move sideways depends on their velocity, spin rate, and degree of tilt (or yaw, as it's sometimes called).
This photo illustrates a crisp and evenly cut crown. You can see the traces of powder residue as it escaped evenly from around the base of the bullet as it exited.