The earth moves under the bullet
A bullet in flight travels in a straight line through space, but the earth rotates beneath it during the seconds it's airborne. From the shooter's rotating frame of reference, the impact appears deflected — this is the Coriolis effect. It's tiny at normal distances and becomes a measurable correction only at extreme range, where time of flight is long enough for the earth's rotation to matter. It is real, it is predictable, and it is the most over-discussed variable in long-range shooting relative to how often it actually matters.
The horizontal component (latitude)
The horizontal Coriolis deflection depends on your latitude and is independent of which direction you're shooting. In the Northern Hemisphere the bullet deflects to the right; in the Southern Hemisphere, to the left. The effect is strongest at the poles and zero at the equator (for the horizontal component). Magnitude is small — at very long range (1000+ yards) it's on the order of a few inches to a fraction of a mil, growing with time of flight and latitude. Conveniently, in a right-twist rifle in the Northern Hemisphere, horizontal Coriolis pushes the same direction as spin drift (both right), so they stack; a good solver handles both together.
The vertical component (Eötvös)
The Eötvös effect is the vertical component of Coriolis, and unlike the horizontal part it depends on your shooting azimuth (compass direction). Shooting east, the bullet impacts slightly high; shooting west, slightly low; shooting due north or south, the vertical effect is essentially nil. The reason: firing east is firing in the direction of the earth's rotation, effectively adding a little to the bullet's "orbital" speed and lift; firing west subtracts it. The magnitude is again small and only relevant at extreme range, but it's the part shooters forget — they'll account for the horizontal drift and miss that an east/west shot also has a vertical Coriolis component.
When to actually care
The honest guidance: Coriolis is negligible inside roughly 1000 yards for practical purposes — well under the noise of your wind and range error. It becomes a genuine, worth-dialing correction in extreme-long-range (ELR) shooting, past 1000–1200 yards and especially toward a mile and beyond, where time of flight stretches to multiple seconds. At those distances a competent solver that knows your latitude and azimuth computes both components automatically, and you should let it.
The error-budget discipline applies hard here (and the Sniper Skillset reinforces it): Coriolis is the last variable to worry about. If you're correcting Coriolis to the inch while your range estimate is loose by 30 yards or your wind call is soft, you've inverted your priorities. Account for it when the shot is long enough that it exceeds your other residual errors — and not before. For the ELR shooter it's a real part of a first-round-hit solution; for everyone else it's a fascinating footnote.