Advanced Classes are the bread and butter of swtor's class 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.
Each class is able to choose from two different specializations at level 10. You should read both of them carefully and even use outside websites/sources for information. The reason you want to make sure you are making the right choice is because once you have made a choice you can't go back. If you are playing a Trooper and you choose Commando over Vanguard by accident you will need to start a completely new character to fix your change.
I can't stress the importance of researching this before the game comes out so you know exactly what you're going to do. As for a bit of self promotion; a good set of class guides to read in helping you choose your class are right on my website actually. You can find them in the Getting Started section or links right now, depending on which allegiance you want, The Republic or The Empire. Keep in mind that while all of the classes are named differently and look different on both factions, the same mechanics are behind all four of them.
Really, all I am trying to say is don't let one class restrict you to a certain faction that you want to play. Your class will be available to both factions, just slightly different on each side. The differences should be subtle, especially since the mechanics are exactly the same. Also, since I was unable to find a list of it anywhere on the interent, here is a list of all the classes in Swtor and what their equal is on the opposite faction.
How Should I Pick My Advanced Specialization?
This is probably the hardest question for anyone to answer, but I will take a swing at it! What you need to do is just find something you will enjoy the most. It's such a dumb thing to say since everyone says it, but it's the truth. I am personally making sure I pick an Advanced Specialization with the ability to tank or the ability to heal. I think I'd lose my mind only ever being able to play a single role. As you already know and since it's been mentioned over and over again, you have to be extremely careful when it comes to picking your Advanced Specialization. Once you choose one of the two options you can not go back. Of course you can choose any of the three specs in that specialization but that may not offer you comfort if you make a mistake here.
As I mentioned before, after you've chosen a class I highly recommend you go to either Torhead or another website that you can look up the specs for that clas and do some indepth research so you know exactly what you want come release day. Trust me on this one, there is nothing worse than leveling up past level 10 only to realize you don't like the specs that are available to you. If you take my advice and want to do research on this before release I highly recommend reading over my class guides as well as using any outside information. Below are a few links that I've used to help me decide which class I wanted to play.
Torhead Skill Calculator - You can read over each and every classes specs here.
Torhead List of Swtor Classes - Clicking on each class will bring you to a page with more information about them. Clicking on the specialization will take you to a page that gives you more information on that.
Almar's Republic Class Guides - Information I have put together myself to assist new players in choosing a class. (This only covers the Republic faction)
Almar's Empire Class Guides - Information I have put together myself to assist new players in choosing a class. (This only covers the Empire faction)
Those are the most helpful links that I can think of giving you for helping you find a class. If you're wondering why swtor's official website is not in with those links it is because I feel that the information it gives you isn't very to the point and informative. Since it's the game's official website they kind of have to take the more advertising route with what they say rather than tell you exactly how it is. I'm not saying it is a bad source of information, all I am saying is that you will most likely be able to find what you're looking for elsewhere and much quicker.