The thing with clothies is that they get killed easily since they generally have low HP and armor. PvP Warlocks deal with this with the use of CC (from both them and their pet), a 20% damage-to-pet mitigation, and specs that give them payloads of hit points. PvP mages deal with it by having obscene kiting measures; you'll have a hard time hitting them. Since priests only have one (30 sec CD) reliable method of CC, no speed boosts, no pet and not a payload of hit points, we need *some* way to ensure we're not gonna die when we get focus-fired. That's where the discipline spec comes in.
Disc focusses on A) Survival and B) Longevity. Going (nearly) full disc pumps your mana and mana regeneration up to insane levels, ensuring that you will not be the one to run out of mana when it's you+DPS vs healer+DPS. Furthermore, disc allows for excellent ways to counter burst damage (which rules PvP); a disc priests' shield can take a payload of damage and there's always pain supression. Borrowed Time ensures that you can get a quick heal off after you shield. Martyrdom and Focused Will are at your disposal to deal with crits. Then there's imp mana burn which allows you to basically ensure that the enemy healer wÃll run out of mana before you do. Power Infusion can be used to allow you to get another extra mana burn off while doing so. And last but not least, there's all sorts of small PvP talents in the tree which do things like reducing stuntime (Unbreakable Will), make your spells nastier to dispel (Silent Resolve) and give you some respite after a critical heal (Divine Aegis).
So basically, even though you said you were clueless, you pointed out the spec's main feature yourself. It offers greatly reduced damage. Which is what we need to get by in PvP. The fact that it also somewhat improves our ability to help partymates survive is why it's picked over Holy. Shadow is another case, but because disc = survival/healing and shadow = DPS you can't really compare the two; too much depends on your bracket and groupmate here.