Bed leveling is two separate things people lump together: tramming (making the bed mechanically parallel to the gantry) and mesh leveling (mapping the warp the probe can't physically remove). Z-offset is the human-set "lower than the probe says" number that controls first-layer squish. All three work together; missing one ruins prints regardless of how well you did the others.
Heat the bed to printing temperature. Tram the four corners with a piece of paper under the nozzle (drag, not friction). Run mesh bed leveling . Print a first-layer test. Live-adjust Z during the print until lines look squished smooth (not stringy, not gouging). Save the offset.
The mechanical foundation. Most modern printers with auto-bed-leveling still benefit from a properly trammed bed — the probe maps surface variation, but if the bed is tilted 1 mm corner-to-corner the ABL probe needs to do too much vertical correction across the print and the toolhead has to keep changing Z mid-layer.
The bed mounts on a 3-point screw system. Use the same paper test, adjusting the three screws to make the bed parallel to the gantry's XY plane. Bambu and Prusa CORE One automate this with a mesh-only routine — you don't manually tram.
The probe touches the bed at multiple points (usually a 4x4 or 5x5 grid) and builds a height map. The firmware then adjusts Z continuously during printing so the nozzle stays at the same distance from the bed surface even where the bed warps.
Probes measure the height of the probe trigger point , not the height of the nozzle tip. The Z-offset is the difference between those two.