Client side Javascript is code which actually runs in your web browser ( Internet explorer, or whatever you use to view web pages ).
Unlike HTML it is used to make more active content. Duo utilise javascript to add both functionality (ie password encryption for example) and more engaging interfaces - image rollovers etc.
We typically reserve the use of Javascript for administrative functionality and members area additions. We do this because javascript can be switched off by your users so if we can't control what users do we only use it in non-critical roles.
Flash has taken over many of the traditional roles of javascript in interface terms, however it is still a powerful tool which can add logic and assist your users whenever they interact with your site.