There are two types of aspect ratios involved in video editing. One is display aspect ratio or DAR; this is the ratio most commonly referred to by the term "aspect ratio", and is the ratio of the video frame's physical (displayed) width to its height, regardless of the number of pixels used to represent the video image. Typical DAR values are 4:3 for standard-definition video or 16:9 for widescreen television.
The other type of aspect ratio is pixel aspect ratio, or PAR (also known as "sample aspect ratio" or SAR). This is the ratio of the width to the height of a single pixel in the video image; a PAR of 1:1 means that each pixel is a perfect square, while a PAR of 2:1 would mean that each pixel is a rectangle twice as wide as it is tall. PAR can be used to refer either to the pixels in a video file, or to the pixels on a physical display device such as a television.
These two aspect ratios are related to each other and the number of pixels in the video frame (or display device) as follows:
DAR width --- = ------ PAR height
When transcoding a video, it is important to take both of these aspect ratios into account. For example, most NTSC DVDs use a video frame size of 720x480 pixels but a DAR of either 4:3 or 16:9, meaning that the PAR is not 1:1. If you transcode that DVD to an AVI file without changing the size, the resulting video may look "squished" in one direction. This is because most video playing software (with the notable exception of MPlayer) assumes that AVI files have a PAR of 1:1, resulting in a DAR of 720:480, or 3:2, for the displayed video frame.
Choosing the proper size for a video when transcoding can be a confusing task. For some examples of how to determine size and aspect ratio, see: Calculating frame size and aspect ratio