On the surface, the term Damage Reduction is rather self-explanatory; it's the amount of physical damage a creature will ignore from every attack. While uncommon, there are examples of flat Damage Reduction, including the sort of Damage Reduction a Barbarian may receive as they level up. Damage Reduction is usually displayed as the number of damage a creature can reduce followed by the type of damage that negates this Damage Reduction. For example, a high level Barbarian may ignore three points of physical damage from every attack, without exception. This would be displayed as 3/-.
Most Damage Reduction is conditional, however, and can usually be overcome by employing a properly enchanted weapon or a weapon made of certain materials against a foe. For example, a Werewolf has Damage Reduction 5/silver, meaning it'll ignore five points of physical damage unless the source is a silver weapon. Much more common is alignment based Damage Reduction (DR 5/good, etc.), or simple Damage Reduction against non-magical weapons (DR 10/magic). Other creatures use Damage Reduction to show resilience to a specific form of physical damage, usually due to the nature of their body. Skeletons, for example, aren't terribly receptive to slashing or piercing damage, but readily take damage from bludgeoning attacks. This is represented as DR 5/bludgeoning.
It's worth keeping in mind that Damage Reduction doesn't effect all forms of damage. A creature with Damage Reduction will still be fully harmed by elemental or magic damage.