As I mentioned before, the 2 major players in the processor field are Intel and AMD. Intel is more popular and has a significant share of the market at over 70%.
You can read more about that here at X-bit Labs.
Anyways, your desktop computers generally hold faster processors than your comparable laptop, since there is more space in your desktop and they can put bigger, faster chips in there.
Your laptop usually has a bit slower chip, because laptops (or notebooks as they like to call it now. The story is that after someone sued for the term 'laptop' after getting his/her laps burned, but that story has to be validated) have to be concerned about power consumption, since people like to use them portably and use them via battery.
You can technically have a superfast processor in a laptop too, but no one will be happy with 40 mins of use on a full charge.
The latest trend are the dual core processors - both Intel and AMD create them.
They are supposed to do the work of 2 processors, and yes, they are significantly faster. But keep in mind that the software also has to be specially written to take full advantage of the dual core technology, so it's not really twice as faster as you might think.
Prices are going down on the dual core processor laptops, so you should be able to get one for under $1000 easily these days. Intel's dual core processors are named Core Duo or Core 2 Duo and AMD names theirs with X2 in the name. Don't worry, they always write on the laptop somewhere that it's dual-core and you won't ever miss it.
That wraps it up, Average Joe. Hope you had an educational, informative time reading this.
And make sure to come back and tell your other Average Joe's and Jane's about this site.