Here's what that looks like.
First you enter two Twitter handles.
Next you can see the conversation between the Tweeps.
You can also just put in one Twitter handle and discover who that person has been having conversations with.
You can also see who is having conversations about a topic of interest.
You can then click on any of the pairings you find to learn what they are saying.
If you are interested in what they are saying, you can even join the conversation, by selecting "reply" right from Conweets.
Conweets is a terrific tool to use in the development of your personal learning network as well as in school when studying areas such as current events. For example, Twitter can allow your students to hear what people are saying but looking at conversations being had in the Twittersphere between interesting Tweeps.