So I am new to World of Warcraft and I have no idea about Professions so I need someone to explain to me -

What they are.
What they all do.
Why do them.
Which most benefits a Rouge.

Thanks.

 http://www.wowwiki.com/Profession
You can have only 2 primary professions at any time. Unlimited secondary professions.

Professions are a good way to make gold and most provide stat bonuses exclusive to that profession. Since you're new, I would go with a pair of professions that compliment each other so you are self sufficient, or you could grab two gathering professions to make gold that way by selling the materials on the AH.
 
Mining/Skinning/Herbalism 
Alchemy/Herbalism
Leatherworking/Skinning

I'm a rogue with mining and jewelcrafting. Learn to play the market and you can make around 20k a week. 

 What they are - Huge timesinks which often offer gear, items or novelty stuff.
What they all do - Cost you time, materials and money, but grant you stuff you can use/sell.
Why do them - Sometimes making items yourself is cheaper then buying it of the Auction House.
Which most benefits a Rouge - There is no make up profession yet, but enchanting uses some dusts and powders in which your 'rouge' should feel right at home.

It depends on if you wan't to make some gear on your own or just get enough cash to buy everything. If you wan't to make gear for yourself the smartest choice is skinning and leatherworking since rogues can only use leather as armor. 
 
I tend to choose two gathering professions so I can earn a lot of gold by selling the stuff I've gathered, my favorite gathering professions are skinning and mining.

Which most benefits a Rouge - There is no make up profession yet, but enchanting uses some dusts and powders in which your 'rouge' should feel right at home. "

MY PROFESSION ! i just went with mining i just could not be bothered doing anything else, it is a great way to get some money from the auction house. 
it also raises you stamina over time

Since you're just starting out I highly recommend going with the mining/herbalism combo.
 
It will net you a good amount of cash. Taking on a crafting profession can be quite expensive and, whereas with the mining/herbalism you can make a good amount of money as you're leveling up (not to mention some respectable exp). Later on in the game you can drop one of the gathering professions for a crafting profession. By then you should know what you want out of a profession and will have a nice reserve of money built up for your epic flying training.

Which most benefits a Rouge - There is no make up profession yet, but enchanting uses some dusts and powders in which your 'rouge' should feel right at home.

I'm a stout Mining/Skinning kind of guy. Then again, I got disgusted at the amount of materials needed for late game professions, so I decided I'll just sell said mats to the crazy people for profit. :) I would say take Skinning over Mining or Herb simply because you'll be killing a lot of things to skin, so there's really no "going out of your way" to get leathers.

That said, if you're going to go with a crafting profession, be sure to choose ones that compliment each other. You don't want Herbalism and Blacksmithing, for example. Pick the gathering profession that compliments the crafting. As a Rogue, I'd steer clear of Blacksmithing, but otherwise you'll benefit at least a slight amount from everything else.

I'd take herb or mining over skinning any day. Skinning every animal you kill becomes downright annoying and I've always made much more cash off of Herb/Mining than I ever have with a skinner.

" So I am new to World of Warcraft and I have no idea about Professions so I need someone to explain to me - What they are. What they all do. Why do them. Which most benefits a Rouge. Thanks. "

Professions are your money makers and avenues to bring more to the table while in groups. After you pick your two professions, you'll have to dicipline yourself to partake in "dailies". This is when you will gather supplies, craft, sell, or generally do whatever you need to do to work on your professions. I don't recommend certain professions like Alchemy or Engineering, they're typically too overwhelming for new players. However, pick things that corispond with your class and professions that complement one another. 
 
For instance, if you're a warrior, go with Blacksmithing so you can make yourself armor. Tag that with mining, so you can gather the items needed to craft armor. If you're a mage or Priest, I almost demand you go with Herbalism and Alchemy. Once again, one of those gather supplies, the other one implements it. The economy also weighs in towards certain professions. When I played WoW, I was making a killing selling specific plants I gathered through Herbalism.

If it's your first character, I'd recommend doing mining and herbalism. This should prove to be a good moneymaker as you level up so you can sell your ores and herbs. Once you're at a sustainable level of money, take up something like Engineering. A rogue with shock paddles is a great addition (and a nice perk) for a group if you choose to do a lot of instances. There's lots of other nice little perks in Engineering, but if you want, Jewelcrafting can offer some good bonuses and items as well.