A desktop-replacement laptop (also known as a power laptop) is just what it sounds like: a larger laptop aimed at people who need the performance and large display size of a desktop computer but want to be able to move the machine from room to room easily. Screen sizes start at 16 inches and go up to 18.4 inches; models with higher screen resolutions are ideal for photo or video editing. Don't expect to carry one of these notebooks around with you all day, though--typically they're too large to fit in a regular backpack, and at 8 to 12 pounds they're tough on the shoulders. Consider these laptops as being more "luggable" than "portable."
The processors in these beefy laptops are typically top-of-the-line, either dual-core or quad-core chips whose performance rivals that of the CPUs found in all but the most powerful desktop computers. Discrete graphics chips from ATI or nVidia are standard on most desktop replacements, too. If you pick the right power laptop, you can play even the most demanding modern games. As for the amount of RAM, 4GB is the bare minimum. A hard drive of 500GB or more is common, while some laptops have up to 1TB of storage.
Of course, all of that power comes at a price. The battery won't last long (typically 2 hours or less with heavy use), so you shouldn't stray too far from an outlet. The high-power CPUs and GPUs run hot, too, making it uncomfortable to rest a desktop replacement notebook on your lap. And then there's the literal price: Cheap models may cost $1000 or less, but a nicely loaded desktop replacement will easily push $2000 or more.
This category is really for two types of people: Gamers, who need tremendous CPU and GPU power to play the latest titles, and professionals (such as video editors, photographers, or engineers) who need large displays and lots of horsepower to do their work.