As you can see from this clip by CommonCraft, Twitter Search is a very useful tool for finding information quickly and easily about a topic of your choice. As it works in real time, it can provide a fascinating insight on breaking news around the world and offer a wealth of opinion about it. You can also use it to keep track of particular followers in your personal learning network, find out what they are talking about and who is replying to them.
Creating an RSS feed of your searches means that you can monitor the results in your reader much more efficiently and track any new developments as they are tweeted.
As an educator, I find following hashtag searches a great way of discovering new ideas from conferences in other countries which I am not able to attend as well as finding new interesting like-minded colleagues to follow.
For some great tips on maximising Twitter Search I suggest you have a look at this article which runs through how to:
choose a topic or combination of topics
find only tweets in your search that contain links
remove unwanted results and spam
filter out (or get only) retweets
create an RSS feed for your query
Have a look too at this post from Mashable on using Twitter's advanced search features.
So if you are finding the information in your Twitterstream is overwhelming at times, try using Twitter Search generated RSS feeds to filter the content you're really interested in and harness the power of the microblogging tool to work for you more effectively.