AviSynth is a powerful tool for video post-production. It provides ways of editing and processing videos. AviSynth works as a frameserver, providing instant editing without the need for temporary files.
AviSynth itself does not provide a graphical user interface (GUI), but instead relies on a script system that allows advanced non-linear editing. While this may at first seem tedious and unintuitive, it is remarkably powerful and is a very good way to manage projects in a precise, consistent, and reproducible manner. Because text-based scripts are human readable, projects are inherently self-documenting. The scripting language is simple yet powerful, and complex filters can be created from basic operations to develop a sophisticated palette of useful and unique effects.

AviSynth works by faking AVI files. That means that AviSynth script files work in principle with all media applications and players capable of opening AVI files. What you might see in real life is that not all applications treat video files like they are supposed to. (For instance, Ligos MPEG encoder will not let you choose anything but straight AVI files in the file selector. But if you load an AVI, and manually change the name in the filename box to .AVS - it works perfectly.)

Because AviSynth works like a frameserver your filters are being applied 'on-the-fly'. That means that when a program that has opened an AVS file requests frame 303, it is read from the source, the filters are applied before the frame is delivered to the program.

If you are already eager to begin, have a look at your First script.

Not all tasks are equally easy to do in AviSynth. In general AviSynth makes it very easy to adjust the look of your video, and doing fast and easy editing. In general it's not easy to use AviSynth for cutting your videos, or doing advanced post-processing. For that it is much better to use programs like Adobe Premiere and Adobe AfterEffects. A very good use for AviSynth is however to prepare your video before you cut it in one of these programs, and adjust color, remove noise, crop / resize.

In general AviSynth is a very good tool when having to compress video. Many filters are written specifically for tasks regarding video pre-processing when compressing or recompressing video. There are many well written plugins to help you make your movie more compressible, reduce noise, adjust color and resize your source material. And because AviSynth works as a frameserver, you often do not need a temporary file before you compress it.
I need a GUI!
Yes, we are talking about video, and it's not possible to make scripts without testing the results. There are some really great programs that support AviSynth or utilize it behind the scenes.

The most well-tested application is VirtualDubMod. It has a great built in editor that allows you to edit scripts and test the result with a keypress. The easiest way to create a script is to create a simple script, open it and enter Tools/Script Editor (or press Ctrl+E). Now you can edit your script and press "F5" to see the result in the main window.

The best GUI solution is DVX it provides complete integration with AviSynth and very powerful GUI's for creating scripts. It provides visual cropping, resizing and many filters. It is able to store the settings for later use so you can reuse the scripts. A definite must-try!

Another powerful, GUI-like approach is AVSGenie. It generates scripts, and allows you to very easy adjust filter parameters visually, and see your result instantly. This is a program with very big potential - only problem for now that it isn't capable of reading scripts, so you can re-edit them.

The license of this software is Freeware, you can free download and free use this video editing software.