Web design is actually a board term that refers to many disciplines and skills used in producing and maintaining websites. There are many areas under web designing such as authoring and web graphic design. Under authoring you have many things such as search engine optimization, user experience design, as well as proprietary software and standardized codes.
One can find many individuals working together as a team each taking care of a different aspect of web designing. It is, however, true that some web designers can take care off all aspects of web designing.
At the beginning web designing did not have much graphics and animation. That is there were mostly text and some simple graphics. The language used for this was mostly HTML. The arrival of Java and Flash, however, changed this. With Java and Flash one could add more graphics and animation, but there was a catch. Flash was proprietary software and not all were happy with this. Also one needed plug-ins to run Flash on their browser.
Then the latest version of HTML that is HTML5 arrived. This again changed the way web designing was done. This technology allowed many things like videos to be run on browsers without plug-ins. Thus, it enabled many people to create beautiful websites without Flash.