As the title suggests the role of the tank in a group is to be the one who has heavy armor and lots of health. The primary job of the tank is to go in first, keep the enemies focused on you so that they won't attack your colleagues In order for a tank to be efficient you will want armor that's going to also allow to have the largest amount of health and other defensive abilities. Many of your abilities are going to designed to have the enemies attention towards you or "Aggro" as it is also referred. Those abilities may consist of "Taunts" or "AOE (Area of Effect)" attacks to keep large groups of enemies focused on you.
This is another import role while in a group. The healer's primary task is to make sure that they keep everyone alive during the fight. Their abilities will be focusing on regenerating health to the tank and other members so that they keep on attacking and take down their foes. Since at times a healer's armor and health points will be low, the group is going to want to make sure that little to no damage is made to the healer. So the tank has to make sure that the enemies are attacking him and not the priest/ shaman who is throwing massive regenerative spells at him. At times a healer might have a small trick up his sleeve so that in case for some instance the tank loses Aggro, they can evade the enemy or stun them momentarily while they re-position themselves and keep on healing the group. And if for some reason a teammate is to fall in battle, a healer will at times have the ability to resurrect that fallen character so they can continue on into their dungeon or instance.
DPS (Damage Per Second)
The job of a DPS is simple but also necessary. Keep on attacking the hard and fast to make sure they go down quickly as possible. For a DPS your weapons and abilities will inflict the most damage. Some times though not often a DPS may switch roles between the tank or healer. A DPS character does have a primary focus but can also be a jack of all trades and will have the ability to fill in various spots while in your group. This tactic at times may not be reccomend so use it very sparingly. But if you find yourself in a group as DPS you have but one objective. HIT VERY HARD AND VERY FAST.
The roles of Tank, Healer, or DPS are only just for small groups. For much larger instances such as Raid where 10-60 players may be involved, it isn't uncommon to find 2 tanks and 4 healers with an army of DPS heroes taking down Gargantuan bosses.
But all these roles all have a primary task in order to survive these difficult dungeons and raids. And this to have open communication with everyone in the group. Make sure everyone is aware of their duties, who and when to attack, what little tricks need to be done and so on. Always be mindful of your surroundings so that you don't wander and attract a large horde of bats that could end up wiping out your entire crew. The best groups and guilds out in the virtual world are the best because they are constantly communicating with one another.
I will attack a video that gives an example of bad communication and overall leadership. It's an older video but also very popular and know in the MMO World. So enjoy the small Onyxia wipe video (Warning: Contains Graphic Language, NSFW)