Hardness is a property of placeables that makes them harder to destroy. When a placeable is damaged, all physical damage and all damage from damage increase effects is reduced by the amount of the hardness. This is similar to damage reduction in that it affects all physical damage. It differs from reduction in that there is no enhancement bonus that can overcome hardness, and in that hardness also applies to some non-physical damage (when that damage comes from a damage increase effect). It is reported in the combat log as "damage resistance".
Since hardness is applied before the plot flag, it can be difficult at times for a player to determine if a given placeable is plot or just really hard. One way to make this determination is to use a weapon that has a non-physical damage bonus (e.g. fire damage, perhaps as an on-hit property from darkfire), as such damage is blocked by the plot flag but not by hardness. It is important that the bonus damage be from the weapon, though, as bonus damage from the character is likely a damage increase effect and subject to hardness.