Basicly for music production you will want a proccesor which is fast, and RAM's to back it up.
A processor is the heart and brain of a computer. The faster the processor is, the faster your computer will be able to send information throughout the system.
A processor is really a brain. Some proccesors more than 1 brain (Also known as a core).
A standard processor might be 3.2GHz, but only have one core. if your computer has 2 cores it will be twice as fast as with 1 core. (I.E if you have a processor with 3.2GHz and 1 core, and a processor with 2 cores with 2.6GHz, it will be equal to a single core processor with 5.2GHz, and therefor the processor with 2 cores is superior)
The names are as follows:
Dual Core - 2 cores / Brains,
Triple Core - 3 cores, brains, triple core processors are pretty rare though
Quad Core - 4 cores, but it is rarely seen on a laptop really. This is pretty common in the newer gaming PC's though.
A fast proccessor is mainly used in a studio enviroment because various VST's drain alot of CPU, and the faster a processor you have, the more CPU you will have available basicly.
RAM:
It's basicly memory for your computer. RAM is used to store temporary information, and while stored this memory is easily accesible by the computer. Ram is mostly used to increase the writing speed on a PC (Like when you music to a CD for example). You can actually compare RAM to the "Short memory span" that a human has. (Im not sure if Short memory span is the actual english word...but you should know what I mean).
I'm using a laptop for my music production. It has 3 Gig RAM and a 2.6GHz Dual Core processor in it, and it works pretty good. Sometimes it does distort a bit when I use alot of effects on my VSTs though.
Since you are going to be using your computer for more than music production I strongly suggest to divide your hard drive in two.
Basicly this means that you instead of having 320 GB of space, you will have one harddisc with 160 and another with 160. (You can do this internally on the computer, you dont need 2 seperate hard discs to this...it can be done only with software modification, just want you to be sure before you go and ask for a laptop with 2 harddiscs

)
The reason for this is you can use one side of the harddisc only for music production, and therefor the CPU/Processor can focus only on your music production and it wont have to use its resources on anything else.
The only downside is when you start your computer you have to choose which side of the harddisc you wish to load...so if you're working on a video and you suddenly decide "Hey, I wanna do some music" you will have to restart your computer to load the other side of the harddisc.

I hope this helped, if you have any questions please dont hestitate to reply
