Yup, party play in most MMO's (and this is not an exception) is based around the so-called "Holy Trinity" of Tank, Healer and DD/DPS (Damage Dealer/Damage per second, the main measure of their performance).
Tanks are designed for 2 things - 1) Getting monster attention and 2) Surviving the beating that ensues. Each monster has a perceived threat from each player - it attacks the player that it sees as the highest threat to it. In this game, the stat for this is enmity. Dealing damage to the monster, and healing damage from it grab enmity. The tank's 1) job is to put out more enmity than anyone else. This is why Gladiators (& later Paladins) and Marauders (Warriors) have certain skills with an "increases enmity" additional effect. It is their compensation for lower damage. How they approach 2) is slightly different. GLD uses the shield to block chunks of damage, MRD parries less with their Great Axe, but can leech lost life back with abilities - plus they have more HP to start with too.
Healers do what they say on the tin - keep people alive! Conjurers (& later White Mages) are the nautral healers, and Scholars can too (as a job from Arcanist - idk if ARC can heal natively). Any class can cross-class Cure from CNJ, but it will have poor potency (possibly Thaumaturge aside. BTW, can a THM cross-class Cure & use Umbral Ice for infinite MP healing? Didn't get to Gridinia this weekend, as I plan to main a LNC).
DDs ... yeah, they deal damage. Kill stuff. Open the pwnage - hence, every 12 year old with a pre-pubescent voice wants to "pew-pew," giving the rest of us a bad name :). They come in 2 types - Melee & Ranged. Melee DD are Lancer (Dragoon) and Pugilist (Monk). Due to needing to be so close, and the danger that brings (being out of range, AoE attacks etc.), they tend to have the highest theoretical DPS, but it is rare to hit that mark. They also get some defensive cooldowns (powerful defensive abilities, that have a long cooldown to restrict their use). Both use combinations of weapon skills to deal their damage, and often must alter their position (side of target, behind target) to maximise their efforts. Ranged DD are Archer (Bard) and Thaumaturge (Black Mage). ACH is still a physical DD, but without positioning requirements as much. THM is your standard caster, with a different mechanic - but it seems from your post you've already rolled one :P. A key THM ability in parties is Sleep. You can remove a monster from combat for 30 seconds - as long as no-one attacks it! Co-ordinate with your group which target you will sleep, to make the tank's job easier.
As others have said, it's beta - it's the time for everyone (devs included!) to make mistakes. Just ... don't go dropping Fire 2's at the tank's feet - they don't like that. And you won't, once 5 mobs start beating on your THM ***!