Advanced Classes are the bread and butter of swtor's class swtor credits advancement. How Advanced Classes works is a bit hard to explain since there really is nothing out there to compare them too. The talent specs for each class do resemble WoW in many ways but the way they make you choose which you want to specialize in at level 10 reminds me a lot more of something along the lines of Aion, Guild Wars or even FFXI.
In those three games you started out as a basic class of some kind and you could better your class, usually at level 10, or you could take up a subclass. A lot of extra information to explain to someone who never played them before. In this case the basic class you start out with is something like a Smuggler or Bounty Hunter. Once you reach level 10 you will still stay a Smuggler or Bounty Hunter but you will have an additional specialization attached to you.
I'm not sure what the Smuggler or Bounty Hunter's specializations are called when you mouse over them in say a PvP situation. But their actual Advanced Classes are called (Smuggler: Gunslinger, Scoundrel) (Bounty Hunter: Mercenary, Powertech).
As I aforementioned, you are able to quickly tell an enemies spec by mousing over them and reading their little pop up of information in the corner. As an example, when you mouse over a Jedi Consular who chose Shadow as his specialization it will read Jedi Shadow. Keep your eyes open for these types of things, this little bit of information could greatly help you in a pinch.