Web standards generally refers to the set of technologies browsers implement to render Web pages, most notably CSS and HTML, though SVG, PNG, ECMAScript, and others are also part of them. Web standards are a good idea as they do not lock you into a single vendor, can be used freely, and will persist for a long time to come.
Proprietary technology has been gaining ground on Web standards in recent years and has been surpassing it on several levels, most notably in the application space and video. Even though proprietary technology has been offering better features for applications lots of them are still written using Web standards, e.g. GMail (Google Mail in Germany, I believe), Twitter, or Yahoo! Maps. Video is a case where proprietary technology is clearly used, e.g. Youtube. (There is also no reasonable alternative.)
Fortunately, the people working on Web standards are working on addressing these gaps. The most signicant effort towards this end started in 2004 by the WHATWG. (For political reasons it could not be done in the W3C initially; they did not believe in an HTML future.) The work started by the WHATWG eventually turned into HTML5, the next version of HTML. Besides addressing significant gaps from HTML4, such as how to properly turn a byte stream into a tree, it is also addressing the Web application space. HTML as a format is already being used all over the place as application format, but it could use some more elements and APIs specifically for this purpose. The effect of that would be that those applications become more accessible and usable, e.g. keep functioning when the user goes offline.
WebSocket, for bidirectional communication with a server. Another effort is going underway to enable communication between two distinct domains, using e.g.
XMLHttpRequest, something that is currently not possible.
These efforts have quite a bit of traction from developers and browser vendors indicating we'll see a lot of this in browsers soon. In fact, quite a bit of what's discussed above is already shipping in (experimental) implementations.