Restoring a cutting edge by removing steel until the two bevels meet cleanly again. Honing has two meanings: Gerber's how-to uses a honing steel to straighten the edge between sharpenings, while Buck's how-to defines honing as abrasion that removes a relatively small amount of material on stones. Most people need both: a stone or system for sharpening, and a rod or strop for honing between times.
An edge dulls three ways: the apex rolls sideways, small pieces chip out, and abrasion rounds the intersection. Honing fixes the first. Sharpening removes steel until a fresh clean apex is formed, which fixes all three.
Bench stones give the most control and remove the least steel. Guided systems hold the angle for you. Pull-throughs are fast, remove a lot of steel and impose their own angle. Rods and strops hone rather than sharpen.
Tapered rods are the only correct tool for serrations, and rods or slack belts are the only ones that work on a recurve.
Ordinary aluminum-oxide stones handle budget and mid-tier stainless. High-carbide steels like D2, S35VN and MagnaCut want diamond or good ceramic.