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Damage Reduction refers to various magic suffixes or special modifiers that reduce damage.

Damage Reduced By (integer)

The effect given from this trait, depending on the level of the item and the suffix itself, is the reduction of physical damage taken from all sources.

In a scenario that a Fallen hits you for 5 damage, ignoring all other penalties, "Damage Reduced By 3" will reduce the damage taken from 5 to 2. It can reduce damage dealt to 0, but will not allow one with such damage reduction to heal from attacks.

The amount reduced is generally too low to be considered useful beyond very early game. Apparently Blizzard had intended this attribute to be standard on some Body Armors, but was later dropped.

This trait exists as a suffix, as such, it is quite common and can spawn on Magic or Rare Items as well as Uniques, Sets, and Rune Words.

Magic Damage Reduced By (integer)

Magic Damage Reduced by X is another form of damage reduction that affects magic damage (Fire, Cold, Lightning, Arcane) rather than physical.

Other than it being magic rather than physical, this attribute works the same way as the previous trait.

Note that non-elemental "Magic" damage (also known as Arcane), cannot be resisted by normal means. However, magic damage reduction will work the same way against it as any other elemental magic.

As with its physical counterpart, this attribute also comes with a suffix and may also appear on most types of items.

Damage Reduced By (percent)

This modifier removes a percentage of the physical damage done to a character, it could be thought of as Resist Physical.

The Über bosses from the Pandemonium Event possess a similar resist damage attribute.

It is generally considered to be a more important statistic than the integer Damage Reduction attribute in spite of the fact it is capped at 50%, normally due to there being little place to stack the former attribute or to utilize Sol Runes as elemental damage is also a concern, especially in later stages of the game. In any case, this attribute is most certainly a helpful one when being attacked by missiles or melee weapons.

Unfortunately, this attribute is also significantly more difficult to find, as it cannot spawn on Magic or Rare Items. The following is a list of items it can be found on:

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