Switchable graphics is fairly simple at the core: the computer has two different graphics cards, one an efficient integrated type (usually Intel Extreme Graphics) and one a much more powerful but less energy efficient discrete card. The computer then switches between them, depending on what you need. Since most of the time you're on the integrated card, you save power, but you still have the power to run more graphics-intensive programs.
In practice, it gets a lot more complicated. There are a few different solutions that I'm aware of:
- nVidia Optimus: This is the official nVidia solution. It is not yet seen in too many machines, and it's still somewhat immature (drivers can be iffy, it's annoying to troubleshoot at the moment). The big upside to Optimus is that it switches between cards 100% automatically, completely transparently to the user. Some people find this annoying, though, because there's no real way to check which card is currently operating, you just have to trust that the system works. On Optimus systems, you can set which card is the default and which card specific programs should run on in the nVidia control panel. Switching between cards really is completetly seamless - no black flash or anything. My understanding is that nVidia achieves this by actually having the graphics cards share a frame buffer, so they both write to the same VRAM for display.
- Hewlett-Packard's system: Many newer HP laptops feature a proprietary system using an Intel integrated adapter and an AMD/ATI discrete. On these systems, there is a simple program that allows you to manually select which adapter to use. The screen will turn off for just a moment, as it completely switches video sources in this system. You can have it automatically go to integrated when the laptop is on battery, but to my knowledge this is the limit of automation - it will not automatically select cards based on software running (e.g. it will not automatically switch to discrete when you start a video game).
- Lenovo has a proprietary solution that works basically the exact same way as HPs, to my understanding. I have not actually used this system.
There are probably other systems out there, but these are the three that I'm aware of. Optimus is probably the best solution, as long as it's working fine. If you have trouble, though, it's probably the most annoying to fix.
Edit: At least Lenovo is now using Optimus in its laptops instead of its older proprietary system. I suspect HP has gone the same way.