A DVD is 720x480 resolution. NTSC itself defines around 525 lines of information, but around 40 or more lines are "useless" information (VBI information, etc). NTSC itself (so-called "Standard definition", SDTV) is 480i ("i" stands for interlaced, and "'p" is progressive).
An interlaced image means that one half (e.g., the odd lines) are drawn first, then the other half (the even lines) are drawn afterwards, forming a full image. A progressive image means that the entire image is drawn in one pass.
All a progressive scan DVD player does is turn a 480i image stored on the DVD (note - you can have either 480i or 480p on a DVD), and "upconverts" it to 480p. If you've messed with a computer DVD player, you may come across the option called "deinterlace" with options like Bob and Weave. That's just the software DVD player transforming an interlaced image into a progressive one (since computer monitors are progressive displays - the interlaced modes are very ancient).
Now, the only way to get true progressive is to use the component inputs. An NTSC image, based on its roots as a black and white transmission standard, has three parts - Luminance (black and white) information, and Chrominance (color) information. A black and white TV just decodes and utilizes the luminance information. Chrominance is used to add color to the image, and consists of two channels - red and blue.
Because of the way it works and the way our eyes work, the luminance information is given "full resolution", and is always the major component of video. Chrominance can be at a reduced resolution but still look OK. Often half or less resolution is used (i.e., the red and blue components can be at half resolution, or 1/4th resolution). It should be noted that most video compression standards use this to pare down the data initially so there's less to compress.
Composite output means both luminance information and the 2 chrominance channels are multiplexed onto one wire. S-Video improves things by putting luminance and chrominance on two pairs of wires (one for luminance, the chrominance with both red and blue multiplexed together). Component gives the best output as each channel gets its own cable and thus is available at full bandwidth.
Of course, the best video yet is to not encode it into this colorspace at all (the technical term is "YUV" color space), and leave it in the RGB color space, which is what your computer outputs and what your monitor takes in. However, it is a lot more difficult to compress an RGB image in a non-image degrading way than a YUV image. RGB inputs on HDTV are taken in through the VGA, DVI or HDMI inputs.
