Twitter's search engine has two important drawbacks: it's limited to Twitter and it sorts the results by date. While there are other search engines like Tweefind that try to sort Twitter posts by relevancy and search engines like Twingly that index multiple microblogging sites, none of them does a great job.
Much like Google Blog Search, Google's microblogging search service will sort the results by relevancy and it also be integrated with Google's web search engine: the keywords that are frequently used in recent posts will trigger a MicroBlogsearch universal search group.
Here's the description used in Google's localization service:
"Recent updates about QUERY. This is the MicroBlogsearch Universal result group header text. A Microblog is a blog with very short entries. Twitter is the popular service associated with this format."
In May, Marissa Mayer discussed the significance of Twitter for Google:
"What's really happening in Twitter is that there are a lot of clues in it in terms of what's happening that's interesting overall. It's similar to what we see in Google Trends, where people will often type what they're interested in into the search box, and we can make some predictions off of that. So we are interested in being able to offer, for example, micro-blogging and micro-messaging in our search. Particularly in Blog Search and possibly in Web Search, but we don't have any particular plans to announce."