If a stream is no longer useful/relevant/outdated, you don't to keep seeing it. Instead you can effectively hide 1-on-1s with a former direct report or file away old private/shared streams. Whatever the case, the mechanism works pretty much the same.
First navigate to the Streams section and click on the stream that you would like to archive.
When the stream is open, you will see a "More actions" button in the upper right corner. This will give you a few options including "Archive this stream"
So what happens when you archive?
The stream will then be tucked away in the Archived section at the bottom of the steam list. You can keep this closed if you want to simplify your view.
And if you need that stream again, open the Archived section at the bottom of the Streams section, open the stream and click More actions --> Unarchive.
(it's the same steps as above, except selecting a different button at the end)