If you use Twitter for microblogging, then you've undoubtedly seen the @reply tag and heard the term 'at reply'. An @reply is a reply to a tweet from one person directly to another that appears in the tweeter's public Twitter stream and in the @reply recipient's @username link (where 'username' is replaced with the person's actual Twitter username) in the sidebar of that person's Twitter profile page.
If you want to reply to someone on Twitter or send a message privately (so the message does not appear in your Twitter stream or the other person's @username link list), then you should use the Direct Message function in Twitter to send a private message.
It's important to note that an @username reference in a tweet only counts as an @reply if it is at the beginning of the tweet. If the @reply reference is made within a tweet, Twitter considers it a 'mention' not a 'reply'. However, both mentions and replies are included in the @username link in the sidebar of a user's Twitter profile.