The ability of a blade to hold an edge. Many people make the mistake of thinking wear resistance and edge holding are the same thing. Most assuredly, it is not; or rather, it usually is not. Edge holding is job-specific. That is, edge holding is a function of wear resistance, strength, and toughness. But different jobs require different properties for edge holding. For example, cutting through cardboard (which often has hard embedded impurities), toughness becomes extremely important, because micro-chipping is often the reason for edge degradation. Whittling very hard wood, strength becomes very important for edge-holding, because the primary reason for edge degradation is edge rolling and impaction. Wear resistance becomes more important for edge holding when very abrasive materials, such as carpet, are being cut.
There are other properties that significantly effect how a steel performs:
Ability to take an edge:
Some steels just seem to take a much sharper edge than other steels, even if sharpened the exact same way. Finer-grained steels just seem to get scary sharp much more easily than coarse-grained steels, and this can definitely effect performance. Adding a bit of vanadium is an easy way to get a fine-grained steels. In addition, an objective of the forging process is to end up with a finer-grained steel. So both steel choice, and the way that steel is handled, can effect cutting performance.
Cleaner, purer steels perform better than dirtier, impure steels. The cleaner steel will often be stronger and tougher, having less inclusions. High quality processes used to manufacture performance steel include the Argon/Oxygen/Decarburization (AOD) process, and for even purer steel, the Vacuum Induction Melting/Vacuum Arc Remelting (VIM/VAR) process, often referred to as double vacuum melting or vacuum re-melting.
Some steels seem to cut aggressively even when razor polished. For these steels, even when they're polished for push-cutting, their carbides form a kind of "micro serrations" and slice aggressively.