You can send a private message to any other user in the slack, or to multiple people.
To start a conversation, either click their name in the left sidebar under Direct Messages for existing conversations, click the + sign next to the Direct Messages to browse for new conversations, or from the chat line simply type /msg @username text_of_message.
When creating a new conversation, you have the option of adding people to it at the beginning by adding multiple names. This is like an impromptu private channel, and only invited members see the contents or know the chat is happening.