Elevation Correction is the result of confirming the elevation shift is mechanically correct and make any necessary corrections to compensate for any deviation.
What is elevation shift
Elevation shift is the amount of travel your POI has at a given distance when the turrets are dialed to a specific elevation or windage
FORMULA - How to determine elevation shift
ELEVATION SHIFT = DIALED ELEVATION x DISTANCE x CONSTANT
Dialed elevation - what you dial on your turrets
Distance is measured from your target TO YOUR TURRETS
Constants: MIL = .03599, MOA = .01047
Elevation Correction Factor is calculated based on your turret's tracking and its ability to track preciously to its value. In other words, if you are using MIL turrets and dial 10 MIL, the reticle should travel exactly 36" (actually 35.99") at a target placed exactly 100 yards measured from the target to your turrets. One way to find out if your scope is calibrated to the exact amount of travel is to shoot a "tall target" test. After doing the test, you divide the amount of travel your scope SHOULD travel (aka elevation shift) by the amount of travel your scope ACTUALLY traveled. What this does is let your ballistic program account for any small error in your turret's travel and make the adjustments for you throughout your shooting solutions.
Many times shooters when testing elevations at yardages find that the numbers on their program do not line up with their action elevations dialed. This can be caused by several factors but the one most overlooked by many shooters is knowing is their turrets are correct. Just because a scope is off in its turret values doesn't mean it's bad scope; many scopes have small deviations and are still within tolerances from the manufacture.