For a long time, PC graphics were available only as a separate card. These days, however, it is possible to get a graphics solution built in or "integrated" with the rest of the processing equipment of the computer. The first chipsets were crude and clumsy, but some of the current examples are decent performers in their own rights. Intel is the current leader in this market, with its graphics-capable chipsets putting up some pretty good benchmarks in the budget class.
Vista and DirectX
DirectX is an API (Application Programming Interface) that allows programmers to access system resources more easily, and with less overhead (overhead equals additional processing power and memory needed). It was originally developed with Windows 95 and has continually evolved, picking up new features over the last decade. For DirectX to work, there also has to be appropriate hardware that can respond to commands from the API. So every time a new version of DirectX comes out, there needs to be new hardware to take advantage of it.
Windows Vista has introduced a new version of DirectX, version 10, which only exists on Vista. Therefore, the current generation of video cards is being designed to take advantage of DirectX 10. Luckily, DirectX is completely backwards-compatible, so a Windows XP system (which can only use DirectX 9) will have no trouble with a DirectX 10-capable video card. Also, Vista is able to run with a DirectX 9-capable card.
It should be noted before we go any further that the Aero interface introduced with Vista is not dependent on DirectX 10 features. However, it does require a certain amount of computing power, and any DirectX 10 card is more than capable of handling it.
Some cards have the ability to receive TV signals and display them on your monitor. This is generally known as a TV tuner card. While somewhat specialized and rare, it used to be fairly straightforward, but is now getting more complicated with the rise of digital TV. For an analog TV signal, a fairly cheap card can do the job, but it will still be best to get a more capable one that can encode the signal into MPEG natively. In addition, you will need appropriate sound output for the TV, which is common in most current systems.