In contrast to SheerVideo, approximating codecs, such as JPEG, MPEG, and DV, bail the file size down by throwing some of the information away and hoping no one notices. Approximating compression is also known as lossy compression, because it loses information. Another name for approximating compression is destructive compression, because it destroys information.
Unless you're into the mathematics of imaging, it may be hard to think of pixel colors in terms of numbers and bits. So let's look at a more intuitive example that everyone understands: text compression. A true, lossless text codec, such as StuffIt or ZIP, shrinks a text file by using shorter codes for commonly repeated phrases and longer codes for rare phrases, but retains all the information to exactly reproduce the original text. A lossy text codec, in contrast, might shrink the text file by capitalizing all the letters, leaving out the punctuation, omitting the vowels, and abbreviating common expressions. Ordinarily, people have very little tolerance for approximating text compression. But in situations where time or space are critical, such as when taking lecture notes or sending a telegram, we're generally willing to sacrifice perfect fidelity.
To take an everyday physical example, consider a suitcase overstuffed with clothing. A true, lossless suitcase compressor fits all the clothing in the suitcase by folding it more neatly, packing it more efficiently, and squeezing it harder until the suitcase can be closed and buckled. A lossy suitcase compressor, on the other hand, cheats by tossing (hopefully) less-important articles of clothing in the incinerator until the suitcase is empty enough to close.
For another example, there are two ways for an advancing piston to reduce the volume of air in an internal combustion engine: either it can truly compress it by increasing the density of the air, or it can fake it by pushing the excess air out through leaky valves and piston rings. Most engineers would object to using the misleading word "compression" for the latter method.
Nevertheless, approximating codecs are still preferable whenever quality is less important than file-size reduction. On the web, for example, many servers and most clients have such slow connections to the Internet that users are willing to put up with very crude image approximations in return for faster access speed.