As you type in the search bar, live results show you autocompleted search queries and people
Hitting enter gives you the full search results, filtered by "top" initially. The "top" search results show you popular Tweets for your search query.
You can filter your search results by Top, Latest, News, Photos, and Videos.
You can filter with extra filters by clicking the "More options" button. Extra filters include things like filtering based on the location of the Tweets.
The extra options also let you save and embed a search, or open the advanced search options.
This more powerful search option lets you do things like exclude search results that include certain phrases.