To be a little more specific, a "conversationlist" is a Twitter list of the people that you talk to (and about) on Twitter.
The list is automatically updated daily, so that it always reflects the people that you are paying attention to right now. If you @reply (or @mention) someone, they're added to your list.
If you stop talking to that person, they drop off your list.
If you create a conversationlist, the people following your tweets can get a little more context: once someone follows your list, it means that they automatically see the tweets from the people that you're sending @replies to, retweeting, or mentioning, so your tweets don't appear in a vacuum.
Your followers see what the people who influence you are saying on Twitter.