Try to visualize the World Wide Web as a topological space with sheaves-like structures mapping semantic content to website pages and to their position in search results. How can this be used by a website to have good stable search results for relevant search phrases, how can the site be optimized for search results, which is the best way for search engine optimization (SEO).
Content is the most important component of a website, and the way it is presented to search engines and browsers. Search engines are accessing more and more of the content that is on the web, Google is parsing and indexing content from Flash files, or AJAX generated, or text from images embedded in PDF files (optical character recognition), This is great for a website's visibility in search results, but it also means that websites have to be carefully structured and designed.
I think that it helps if a website is as simply designed as possible, and uses new features available. For example, until recently, a way to solve the canonical URL problem of URLs with www and without www (when search results oscillate between one version of URLs to the other, affecting position in search results), was to set permanent redirects HTTP status 301 in the server header from one type of URLs to the preferred one. Search engines introduced recently support for a <link rel="canonical> element that solves this problem, so there is less load on the server and shorter time response.
Search engines are continuously adapting the way they index websites and present them in search results. They do not like to be cheated, by keyword stuffing, or systematic link exchange, or by hidden text. Content is the most important aspect of a website.
The world wide web is in continuous flux, there are new websites all the time, the way websites are built changes all the time. The use of AJAX, of embedding video and sound in websites, embedding news, blog feeds, and all kinds of gadgets like weather reports or interactive maps, designing websites for mobile phones, all these are making the world wide web very interesting and useful.