Damage Reduction
Damage Reduction, is a game mechanic popularized by Dungeons & Dragons, although it wasn't formally named as such until 3e. As the name probably indicates, Damage Reduction is a way of handling the various supernatural or logical toughness-related advantages that different creatures may have, resulting in a reduction of damage inflicted, unless the damage was caused by something specifically useful for hurting that creature.
The two most classic examples are skeletons being resistant to non-bludgeoning physical damage (but taking bonus damage from blunt hits) and werewolves being super resilient, if not outright immune, to any damage that isn't inflicted by a silver weapon. This is usually rendered as a set number that all incoming damage is reduced by, typically rendered thus on a stat block: DR/X - Y, where X amount of damage skimmed off the top of any incoming damage not inflicted by Y and Y is the nature of the weapon or damage type necessary to ignore the damage reduction. For instance, a wererat might have DR/5 Silver.
Energy Reduction follows the same principle, but specifically applies to one (or, in some creatures, more than one) form of elemental damage. For example, a demon taking less damage from fire, or a yeti taking less damage from ice.
This is distinct from damage immunity, which prevents all such damage outright.
While Pathfinder, in keeping with its status as the Hackmaster of third edition, kept the old Damage Reduction system, it did introduce rules whereby sufficiently-powerful weapons pierced certain kinds of DR just by increasing in enhancement bonus. This is the source of much civilized and respectful debate, with some arguing it's conceptually stupid and cheapens the exotic materials, while others argue that, from a gameplay perspective, having so many different materials wasn't adding that much anyway and really hurt certain styles of play, like dual-wielders.
Notably, while previous editions (and Pathfinder) use this system exclusively, 4th edition instead introduced Damage Resistance, which instead halves all damage of the relevant type, and also used it exclusively. Fifth edition mostly uses the 4th edition method, though a very small number of feats and monster powers use the old-tyme damage reduction in a limited way, though not usually called that. It also tends to give all magic weapons the flat benefit of penetrating damage resistance and reduction of any kind.
Notably, the two systems actually incentivize different methods of play a little. For instance, Damage Reduction penalizes dual-wielding in a number of subtle ways, including but not limited to having to maintain twice as many weapons to deal with it and being disproportionately affected by it, since having ten skimmed off the damage of each attack hurts the guy who swings four times for less damage more than the guy who swung once but hit really hard. Conversely, since Damage Resistance halves all damage, it swings in the other direction a little, though not as dramatically.