A private chat window with another user is called a query window. In mIRC you double-click on a person's nickname to open a query window - in older, text-based IRC programs you had to type /query nick, hence the name. Note that you can still talk to someone in a query window even after you have left the channel you were in. In fact, you can open up a query window to someone even if you aren't in the same channel as they are. As long as you know their nickname, and you know they are on-line, you can type /query theirnick to initiate a chat.