The search box suggests titles as you type. If there were a language selector next to it, you could search through the list of articles in that language. Aha, but you say, what's the point of that? If I wanted to read about "Green Eggs and Ham" in Italian ("Prosciutto e uova verdi"), I would go to the Italian Wikipedia and read it there. Well, that's not what I'm proposing; what I mean is, if you selected Italian and searched for "Prosciutto e uova verdi", you would get taken to the English article, "Green Eggs and Ham".
When you type in the search box, it sends an Ajax request off to what I imagine must be an API somewhere for the Wikipedia database which responds with a list of matching article titles. I don't know what the syntax is for that request, so here's some pseudocode for the purposes of illustration:
Suppose we select Italian and start searching for "prosciutto e". The API call is:
We get one result back, "Prosciutto e uova verdi". As we're operating with Italian selected, clicking it sends the API request:
API?action=showarticle;titlelang=it;title=Prosciutto e uova verdi
That returns "Green Eggs and Ham" and sends the user there.
Of course, this requires a complete table of interlanguage mappings. If I understand it right, that's something that will eventually be provided by Wikidata.