What are holdover and holdunder, and why does an airgun need them?

Pellets travel on a steeply curved (parabolic) arc compared to a high-velocity rifle bullet.

Most airgun zeros produce two crossings of the line of sight: a near zero (e.g., 15 yards) and a far zero (e.g., 35 yards). Between those, the pellet is above the crosshair and you hold under the target slightly. Beyond the far zero, the pellet drops and you hold over. A mil-dot or BDC reticle gives you reference points for these holds. The bigger and slower the caliber, the more dramatic the holdover.