Right now, there is the option to add featured topics to the left-side menu. It is explained here: https://community.tribe.so/question/5cd31d4a2014660640dd2d4c49
Also, if you are using the Groups features, when a community user is a member of a group, he will see the list of his groups on the left navigation as well.
To add other sections to the left navigation, you need to use the Admin Panel> Theme> Advanced Setting> add the related CSS code and HTML code to add more stuff to the navigation.
For example, a customer has used the HTML coding to add some posts from their company's tweeter to the side menu: