Conversations are determined by the ratio of @-reply tweets to all tweets, that means tweets that are interactions with other Twitter profiles. This indicator is especially relevant for service providers, it shows at a glance how high the rate of conversations is. A high conversation rate is interesting for everyone, since like all social networks Twitter lives only through interaction with other users.
The higher your conversation rate, the more involved the account is in direct discussions. A moderately high conversation rate by an account that is not geared towards service indicates a well connected and active profile.