The thing you're looking for is circles.

1.) Click on the people shaped "Contacts" icon up top.
2.) Select the "Circles" tab on the upper right side of the menu bar.
3.) On the left, next to "Circles", click the plus sign to create a new circle.
4.) Enter a name for the circle and press enter.
5.) Click the plus sign to the right of the people you want to add to that circle.
6.) Return to the square shaped "My friends conversations" icon up top, and select the circles you want to view.

Alternatively, you can search for an item (either a search term of a hash tag), and then there is a floppy disk sign on the upper right to save the search. That is then available in your friends conversations screen under "Saved Searches".