Bore axis

The recoil from a fired cartridge (and the action movement) exerts a rearward impulse along the bore axis, which is commonly above the center of mass of the gun.

This force couple creates a rotational torque around the mass center and make the gun pitch upwards after each shot — a phenomenon known as muzzle rise.

A lower bore axis will align more of the recoil directly into the hand, creating less couple torque and thus less muzzle rise.

Handguns lack a buttstock to aid in recoil control, so design elements that reduce felt recoil or muzzle flip are considered highly desirable and numerous manufacturers claim their handgun design has a low bore axis, although few offer measurements to prove this claim.

[2] Handguns such as the CZ-75, which combine a heavy steel frame with a low bore axis (relative to other hammer-fired guns) achieve twofold reductions to felt recoil and muzzle flip, and are popular choices in many competitive shooting disciplines.

The AR-15 is an example of a weapon system where the sights are high over the bore.
Browning BAR is an example of a weapon system where the sights sit low and close to the bore.
The Chiappa Rhino is an example of a pistol with a low bore axis.
The SIG Sauer P226 is an example of a pistol with a high bore axis.