Clothadin is a term used to describe a paladin who wears cloth armor to increase their healing abilities. Since the only benefit of plate is increased mitigation of physical damage and healers don't take part in melee, a large number of paladins have been known to wear cloth, leather as well as shaman mail armor. This was more popular prior to The Burning Crusade expansion, when the best cloth and leather healing equipment was significantly better than the best plate healing equipment available. Since the release of The Burning Crusade, good plate healing gear is a lot more common. Often times paladins will wear any gear that strongly benefits healing, regardless of the armor type. Some paladins may keep cloth armor only for certain bosses where they know they will not receive melee damage, like for the final boss of Shadow Labyrinth, Murmur.
Since many cloth items yield high intellect bonuses, a primary attribute for paladins, it is not uncommon for them to wear one or more pieces of cloth armor, especially when they are the main healer for a group and their ability to heal becomes critical. While wearing cloth armor can certainly increase a paladin's mana reserves, it also causes them to take more physical damage when struck in combat. This makes preventing mobs from attacking a clothadin even more important for the group's tank. It is advised to protect clothadins at all costs, because they are squishy and will likely die first.
For any paladin considering wearing cloth armor, it is important to always keep a spare set of plate armor on you. When in a party that is struggling with particular mobs, switching to plate armor can give the other members of the party a few more seconds to pull mobs off of the healer before they die, thus making a wipe less likely. But if you need the cloth armor for healing, it is wise to keep it for the instance.
Clothadins tend to be more common on servers with a low priest population. Nevertheless, clothadins should be extremely tactful in deciding to roll on loot if another member of the party (especially priests or druids) wants the item, even if the other member only heals as an off spec.
Now that Paladins have Plate Specialization it might not be worth using non-plate armor anymore.