Twitter search is one place where you can make the most of twitter, and use it in many ways, some of which are

-Finding new friends talking about something you too are interested in
-Finding clients/customers for your company
-Searching for feedback on companies
-Get involved into discussions
-Searching for tweets related to the most popular topics aka trends
-Search for tweets from local areas to filter out any news
Hashtags for certain events/news categorization

So, to get more involved in twitter and do the best with twitter search, here are a few good tips to use:

1)Use the advanced search
2)Location searches for particular keywords
3)Combine words into phrase

Good luck..