In Twitter, Direct Messages are a way to send a private message to a particular user.
To do this, in your Dashboard, locate a post from the user you wish to Direct Message. Hover over their post and the settings wheel located in the top right corner of the post. Select the Direct Message option in the menu that appears.
Then a popup will appear where you can select the Twitter account you'd like to send the message from, and the name of the account you're sending the message to. If you can't find a post of the user you wish to Direct Message in any of your panels in your Dashboard, you can just click on the Direct Message option on anyone's post to Twitter, and edit the To: field in the popup with the username of the Twitter account you would like to message. Remember, Direct Messages are private messages and will not show up publicly on Twitter. Also, remember to stick to under 140 characters even in Direct Messages.