You can choose to hold private conversation with people through the Private Messaging (PM) feature. The private messaging system allows forum members to communicate one-on-one in private, like email, but hosted on the forum. You can also choose not to participate in this. It's controlled in your User CP.

You can create a Buddy list. When userids have been added to that list, clicking on the Open Buddy List link at the top right side of the screen brings up the last time each was online, and gives a shortcut way to send one a private message (if the person is set up to allow private messages). Adding userids to your Buddy list is done in your User CP in the Miscellaneous category on the left-hand side of the screen.

You can ignore user IDs of those people whose posts you are not comfortable reading. This is also done in your User CP in the Miscellaneous category on the left-hand side of the screen. Even post titles by this userid then do not appear on your screen.