You cannot use VLC to burn DVDs/CDs, however you can convert the video into other formats that may be more suitable for e.g. making a DVD-Video, although ordinarily it shouldn't be necessary.
If you are running Windows and wish to write an *.avi to a DVD-Video then you could try something like
DVD Flick which is able to do that (development version can create menus). For writing data (CD/DVD) discs on Windows try e.g.
InfraRecorder.
Cheers, Arite.