There are no skill trees like Sagittarian said.
However, when you get to level 10 you unlock the potential to change your class / job to something else. By leveling all the classes, you unlock their abilities, and you can cross class them.
For instance, you're a Marauder currently. Marauders become Warriors. To become a warrior, your marauder has to be level 30 and I believe gladiator has to be 15. Then the quest to become a Warrior can be unlocked.
To become a BETTER Warrior, people will expect you to have certain abilities, like for example, Provoke. Provoke is a Gladiator ability. So you'll find yourself leveling up Gladiator a bit in order to unlock and then "Cross class" the ability Provoke onto your Warrior.
Get it?
Also, something you need to understand now or you'll get confused later:
The base "classes" you get are referred to as exactly that - Classes.
The advanced "classes" that you unlock at Level 30 are referred to as Jobs. In typical Final Fantasy games, the term "Job" is used to refer to the classic icons like Warrior, Paladin, Dragoon, White Mage, Black Mage, Bard, Scholar, Monk, Summoner, etc.
Jobs are designed around party play, and Classes are designed more for solo play.
Classes can cross class almost any ability from any class you unlock / level up.
Jobs can only cross class abilities from two other CLASSES.
Jobs can not cross class other JOB abilities.
In FFXIV 1.0 this was more important because soloing enemies was very tough as a JOB. The reason:
Example:
Enemies were tougher to defeat in the field, so If you were Dragoon, you'd have to remove your soul crystal to revert back to Lancer so that you could cross class Cure, if you had it. (From Conjurer) A Dragoon can not cross class abilities from conjurer, but Lancer can.
in FFXIV 2.0 - Now obviously known as A Realm Reborn - Enemies in the field are chumps, and you can basically do anything and everything on your JOB. And nearly everyone just stays on their JOBS. However, reverting back to your class wouldn't hurt when you're solo. The way the game is designed now, JOBS will eventually become completely superior. Even more so than they are now. Another thing to note is you can not wear gear that is only for your JOB, nor can you use JOB abilities when you're on your CLASS.
I hope that makes sense to you. As you press on it'll become clearer.