of course you need to have a good database with relevance-info and search-algorithms on the server. And of course this isn't a feature for a private homepage with few pages like "This is me, these are my hobbies, this is my dog,...", but for big professional sites like Wikipedia, and so on.
Big sites like Wikipedia, Google, IMDB, ... can make this feature that they're providing already today, more accessible to more users. Small sites don't need to use this feature, or they can use professional services, like they do today for providing a search box on their sites. And of course, the classic search without suggestions should be available further on.