VBR

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Variable Bit Rate, as opposed to Constant Bit Rate or Average Bit Rate, is a type of stream whose bitrate (number of bits per unit of time) changes as necessary.

Video

Practically all video codecs are VBR by nature. In a 1-pass encode, bitrate is distributed as the codec sees fit, meaning that you can have uniform quality, but no control over final filesize. In a n-pass encode, the scene information from the previous pass is logged and used to calculate how to distribute bitrate, so quality is uniform and final size is very close to intended.

Streaming videos are usually CBR or ABR.

Audio

Though MP3s are traditionally CBR, VBR MP3 files are gaining popularity recently. Many other audio codecs are nativelly VBR, such as Vorbis and AAC. AC3 is CBR.

VBR Audio and AVI

The AVI container was not originally designed to support VBR audio. In order to support this, a hack indexes the audio stream as if it were a video stream, thus allowing VBR MP3 and AAC files into AVI. Recently, AVI-Mux GUI added support for Vorbis audio into AVI as well.

Most programs that can edit AVI will not work as expected if there is a VBR audio track in it.