Let's face it, none of us can realistically keep up with the thousands of accounts we follow or that follow us. Twitter Search will make it much easier to get to the good stuff, the stuff that's important to you.
While the basic version of Twitter Search works like most other search bars, it's important to know the search operators so you can quickly narrow your search to find what you're looking for. Twitter search operators work in a similar fashion to Google Search Operators but do vary a bit.
To see the Twitter Search operators just click "Operators" underneath the search bar.
If you're new to Twitter Search a slightly easier way is to use the "advanced search" option which allows you to populate fields rather than having to know the actual operators. However, I'd advise looking at the operators so you know what options are available.