Twitter's search capabilities are one of its most useful features, but only let you look through actual posts on Twitter. TweepSearch extends that capability to allow you to search through the information in individual profiles.
As Twitter specialist blog TwiTip points out, this can be a useful feature if you want to locate people on Twitter with a particular job (like journalists or gardeners). You can also use it to find comments by people who are friends with a particular individual.
Concerned about the privacy implications? Remember TweepSearch can't search for information that's not already there. (Ultimately, though, Twitter is a public medium, so stick with Facebook or other social networks if you want a stronger degree of privacy controls.)