Fluxus is an environment which allows you to quickly make live animation and audio programs, and change them constantly and flexibly. This idea of constant change (flux) is where it's name comes from.
Fluxus does this with the aid of the Scheme programming language, which is designed for flexibility; and an interface which only needs to provide you with program code floating above the resulting visual output. This interface enables fluxus to be used for livecoding, the practice of programming as a performance art form. Most users of fluxus are naturally livecoders, and some write fluxus scripts in front of audiences, as well as using it to rapid prototype and design new programs for performance and art installation.
This emphasis on live coding, rapid prototyping and quick feedback also make fluxus fun for learning computer animation, graphics and programming – and it is often used in workshops exploring these themes.
This manual is vaguely organised in terms of thing you need to know first being at the beginning and with more complex things later on, but it's not too strict so I'd recommend jumping around to parts that interest you.