First up is the Weakened Armor debuff. Essentially, this is the old-school Sunder/Expose Armor affect. It's gone entirely. Rogues no longer have Expose Armor, warriors no longer have Sunder Armor and the Devastate prot warrior ability no longer applies Weakened Armor. In addition, the druid ability Faerie Fire now applies Physical Vulnerability instead, increasing all physical damage taken by its target by 4% for 30 seconds. This is because it was thought that having both Weakened Armor and Physical Vulnerability was excessive, since they did basically the same thing. What this means in terms of how we play? Almost nothing. If you're a rogue, you won't use Expose Armor anymore because it's gone. A warrior tank will hit Devastate the same as they always did. Druids are still going to use Faerie Fire to debuff things. Hunter pets that had similar abilities will no longer have them.
Next up is the Weakened Blows ability that almost all tanks had - it reduced incoming damage. The abilities that provided it still exist, they simply don't provide it anymore. Thunder Clap is an example of an ability that currently provides the debuff, but won't in Warlords. Since all tanks applied this debuff, it basically wasn't very meaningful, and instead monsters will simply be tuned to do less damage to compensate for its removal. What changes for players? Nothing. You won't apply the debuff, but you'll still use those abilities that did once apply it.