One of the most irresistible-to-ignore differences between Google Plus and Facebook/Twitter is that Google Plus has no provision of messages, inbox or direct/private messages. Google+ has a single home screen, which lists the entire message/share stream just like the Facebook news feed. Within the same home screen, you can share stuff to all or send private message to anyone.
#. How to send direct or private message
1) Compose your message in the share box at the home screen stream.
2) Set the visibility of the message only to the person whom you intend to send. To set the visibility, type the name of the person in the second box. As soon as you start writing his/her name, Google Plus will automatically show you suggestion from which you can easily choose.
3) Click on the share button and you are done.
Note: The receiver should be in your circle, or else his name will not appear in drop-down suggestions. In addition, you can also send the same message to multiple people using the same process.
To verify that the message is between only you two, hover your mouse to Limited keyword next to your name. There you will find the number of people that can see the message. [As shown in above image]