So what does a real time search engine mean/do? Well, basically people are starting to use Twitter to talk about brands in real time. Twitter added the search field recently which is a way of keeping users on the page as they continuously look at topics, brands and trends depending on what's in the news etc.
Therefore a well-implemented real time search engine can bring users together to talk about particular brands and trends which makes it easy to target advertisements against them. Twitter has already started experiments with ads by placing a small unit right below your profile and stats.
So to put it simply: You're watching a football match, you do a real time search on one of the teams, you find like-minded people and exchange views etc. while there are ads on sporting goods on the page. Advertisers can then implement strategies quicker and more effectively.
Twitter's traffic figures are growing exponentially, with numbers growing 3000% in the year from February 2008 to February 2009.
See also: Google rumoured to be buying Twitter and Google in late stage talks to buy Twitter