The ballistic coefficient of a projectile is a measure of the ability of that projectile to maintain velocity through air of a given density. Projectiles with high BCs experience less aerodynamic drag than those with lower BCs and therefore lose velocity more slowly.
If you have two projectiles that leave the muzzle at the same velocity but have different BCs, the one with the higher BC will cover any given range faster and therefore will have less drop due to gravity over that range. Lonestar driver was nearly correct in that the BC of a bullet is dependent on its shape and diameter, but it is also dependent on the projectile's mass. Bullets of a given caliber with greater mass have a higher BC than those of lower mass, given exactly the same shape. Conversely, bullets of greater diameter experience more aerodynamic drag given the same shape and mass as those of lesser diameter and therefore have lower BCs.
The concept of a static ballistic coefficient has some fundamental flaws. It is based on a "fixed drag" model and, unfortunately, the ballistic coefficient varies with velocity. But it works well enough to be useful although some accommodations need to be made when shooting at very long range. Another problem with the ballistic coefficient is that in addition to projectile diameter (caliber) and mass it is dependent on a "form factor". That is where the shape of the bullet enters in. The form factor is the ratio of the aerodynamic drag coefficient of the bullet you are shooting to that of a standardized "test bullet" of a specific shape. If the shape of the bullet you are shooting matches that of the test bullet closely you can assume that the curves of the aerodynamic drag coefficients of the two bullets remain proportional (parallel) over the entire range of bullet velocities.
Unfortunately, that is often not the case. The BC of 0.267 that you cited is based on the G1 drag coefficient. That uses a rather antiquated standard projectile shape that is more like a modern pistol projectile than a modern rifle projectile. So as projectile velocity drops, the aerodynamic drag coefficient curves of the bullet you are shooting and that of the G1 standard projectile start to diverge. Still, the G1 ballistic coefficient is what most projectile manufacturers use and it is still widely used by most ballistic computational software.
Another issue is that aerodynamic drag is not a constant for any bullet of fixed mass, diameter, and shape traveling at any given velocity. It is dependent on air density. Air density is determined by air temperature and local atmospheric pressure, and to a much lesser extent, by relative humidity. Unless you are shooting at very long distances, the relative humidity won't make a difference, but air temperature and barometric pressure will. Ballistic coefficients are based on "standard atmospheric conditions". The standards most often used by bullet makers and ballistic software programs assumes a local barometric pressure of 29.92 inches mercury at mean sea level, a temperature of 15 degrees centigrade (59 degrees Fahrenheit) and a relative humidity of 0%. But if the air temperature when you are shooting is different or the local barometric pressure is different, the air density will be greater or less than standard and the observed ballistic coefficient of your projectile will not correspond to the stated BC.
So ballistic drop compensation reticles, sights, and turrets are really only accurate for a specific cartridge at a specific muzzle velocity, and with atmospheric conditions that conform to the standard. Local barometric pressure varies quite predictably with altitude. The average local barometric pressure drops by approximately one inch of mercury with each 1000 foot gain in elevation. So the standard atmospheric pressure is 29.92 inches of mercury at mean sea level, but only 24.89 in Hg at 5000 feet. That difference will result in a big drop in air density and corresponding increase in observed ballistic coefficient. Each one percent change in atmospheric pressure will result in a corresponding one percent change in observed ballistic coefficient. If you know the elevation at which you will be shooting and can estimate the local average temperature of the season you will be doing most of your shooting, you can use a ballistics program to tailor your bullet's BC accordingly. Tailoring the BC is what ballistic software programs do to adjust bullet drop and bullet velocity for local air density.
So whether or not it is worth changing the turrets on your scope will depend on a lot of factors. First, is your observed muzzle velocity accurate? If you can I would confirm it with another chronograph. Second, will you be shooting in conditions that depart very significantly from "standard" conditions? If you live at significant elevation and plan to do much shooting in weather warmer than 59 degrees F, the air density will be significantly less than the "standard" air density that the BC is based on. High levels of relative humidity also decrease air density a little bit, especially at very warm temperatures. If your actual muzzle velocity is less than what your scope manufacturer based the turret adjustments on, but the air density is significantly less than the standard that the bullet maker based the BC on, the two may cancel each other out to some extent.
Lastly, what ranges do you expect to be shooting at? Small departures from standard muzzle velocity and air density might not make much difference shooting at 200 yards, but make a big difference if you are planning to shoot out beyond 600 yards. But if you are planning to shoot much beyond 400-500 yards you probably won't be shooting 55 grain .223 Remington.